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B1 noun 10分钟阅读

مجذور

majzār
例句 مجذور 30秒了解
解析 مجذور in your Level:
At the A1 level, you don't need to use the word 'majzoor' often, but you might hear it in very basic math contexts. Think of it as 'multiplying a number by itself'. If you know numbers like 1, 2, 3, then 'majzoor' is just the result of 2x2 or 3x3. It's a special name for a specific kind of multiplication. At this stage, focus on the sound: 'Maj-zoor'. Imagine a square box and a number inside it. That's the 'majzoor'. You won't be expected to use it in conversation, but seeing it in a textbook shouldn't scare you. It's just a fancy way to say 'squared'.
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At the A2 level, you start to learn more specific nouns. 'Majzoor' is one of those words that helps you move from basic Persian to 'school Persian'. You might use it in a simple sentence like 'The square of two is four'. You are beginning to understand that Persian has special words for math, just like English does. You should be able to recognize the word in a simple math problem. If a teacher says 'Calculate the majzoor of five', you should know they want you to do 5 times 5. It's a useful word for describing simple patterns or areas of small shapes.
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At the B1 level, you are expected to use 'majzoor' correctly in academic or professional settings. You understand the difference between 'majzoor' (the square) and 'jazr' (the square root). You can explain a simple formula using this word. For example, 'To find the area of a square, calculate the majzoor of its side'. You are comfortable with the 'Ezafe' construction: 'majzoor-e in adad' (the square of this number). You also start to see the word in more complex sentences, perhaps in a news article about science or technology. This is the level where the word becomes part of your active technical vocabulary.
At the B2 level, you can use 'majzoor' in complex scientific discussions. You are familiar with the plural form 'majzoorat' and can use it in contexts like 'the sum of squares'. You understand how the word is used in physics formulas (like the inverse square law). You can distinguish between 'majzoor' and 'morabba' (unit/shape) with ease. Your pronunciation is fluent, and you can use the phrase 'be majzoor resandan' (to square) in a variety of grammatical tenses. You might also encounter the word in literary or metaphorical contexts, where something increases at a 'majzoor' rate (exponentially).
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At the C1 level, you have a deep understanding of the word's etymology and its place in the history of Persian science. You can discuss the works of Al-Khwarizmi and how he used these terms. You are sensitive to the register of the word, knowing exactly when to use 'majzoor' versus 'tavan-e do' to achieve a specific tone in your writing. You can read advanced academic papers in Persian where 'majzoor' is used in the context of advanced statistics, quantum mechanics, or engineering. You can also identify and correct subtle misuses of the word by others, demonstrating a near-native grasp of technical Persian.
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At the C2 level, 'majzoor' is a word you use with complete precision and stylistic flair. You can engage in high-level debates about mathematical terminology or the translation of technical concepts between English and Persian. You understand the philosophical implications of 'roots' and 'squares' in classical Persian thought. Whether you are writing a textbook, delivering a keynote at a scientific conference, or translating a complex technical manual, you use 'majzoor' and its related forms (like the plural 'majzoorat') with total accuracy. You are also aware of rare or archaic uses of the word in historical manuscripts.
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例句

مجذور 30秒了解

  • Majzoor means 'squared' in Persian math.
  • It is the result of x multiplied by x.
  • Commonly used in school and scientific contexts.
  • Distinguished from 'jazr', which means 'square root'.

The Persian word مجذور (majzoor) is a fundamental mathematical term used to describe the result of a number being multiplied by itself, commonly known in English as a 'square' or 'squared number'. Derived from the Arabic root ج-ذ-ر (j-z-r), which pertains to roots and foundations, the term literally translates to 'that which has been rooted' or 'the result of the root operation'. While in modern English we distinguish between 'square' (the result) and 'square root' (the base), in Persian, مجذور specifically refers to the product x². For example, if you take the number 3 and multiply it by itself, the result is 9; in Persian terminology, 9 is the مجذور of 3.

Mathematical Context
In academic settings, from primary school arithmetic to advanced calculus, this word is the standard way to denote the second power of a value. It is used in formulas, geometric calculations (like finding the area of a square), and statistical analysis.

عدد نه مجذور عدد سه است.
Number nine is the square of number three.

Understanding this word is crucial for anyone studying STEM subjects in Persian or engaging in technical professions. It is more formal than the colloquial expression به توان دو (be tavan-e do), which simply means 'to the power of two'. When a mathematician or an engineer speaks, they will almost certainly prefer مجذور. This term also carries a sense of precision and historical weight, linking modern Persian math to the golden age of Islamic science where scholars like Al-Khwarizmi laid the foundations of algebra.

برای محاسبه مساحت، باید طول ضلع را به مجذور برسانید.
To calculate the area, you must square the length of the side.

Daily Life Usage
While not common in casual grocery shopping, you will encounter it in real estate (calculating square footage), construction, and even in some metaphorical literary contexts where something grows exponentially.

فاصله با مجذور زمان متناسب است.
The distance is proportional to the square of time.

Beyond the classroom, the word appears in coding and programming documentation in Persian. If you are reading a technical manual for a software library in Iran, functions related to squaring a number will often use this root. It represents a level of literacy that moves beyond basic counting into the realm of logical and scientific Persian. Its usage marks the speaker as educated and precise.

مجموع مجذورات خطاها را کم کنید.
Minimize the sum of the squares of the errors.

Linguistic Nuance
The word follows the 'Maf'ool' pattern in Arabic morphology, which indicates a passive state. It literally means 'that which has been made into a root/foundation', reflecting the ancient view of the square as the foundational area of a root length.

در این فرمول، سرعت به صورت مجذور ظاهر می‌شود.
In this formula, velocity appears as a square.

Using مجذور correctly requires understanding its role as a noun that often acts as the object of a mathematical operation or a descriptor of a value. It is frequently paired with the preposition عدد (number) or used in the 'Ezafe' construction (majzoor-e...). When you want to say 'the square of X', you say مجذورِ X. This structure is the most common way to integrate the word into a sentence.

Common Verb Pairings
The most common verb used with this word is حساب کردن (to calculate) or به دست آوردن (to obtain). In more formal proofs, you might see رساندن (to raise/to bring to), as in 'be majzoor resandan' (to square something).

او مجذور عدد پنج را به سرعت حساب کرد.
He quickly calculated the square of number five.

In scientific writing, مجذور often appears in the plural form مجذورات (majzoorat), especially in statistics when referring to the 'sum of squares'. This follows the Arabic feminine plural ending '-aat', which is commonly used for technical terms in Persian. If you are discussing the 'Least Squares' method in regression analysis, the term used is کمترین مجذورات (kamtarin majzoorat).

مجذور هر عدد منفی، عددی مثبت است.
The square of any negative number is a positive number.

The 'Be Majzoor Resandan' Construction
This is a compound verbal phrase. 'Resandan' means 'to deliver' or 'to cause to reach'. So, 'to cause a number to reach its square' is the formal way to say 'to square a number'.

اگر این متغیر را به مجذور برسانیم، رابطه خطی می‌شود.
If we square this variable, the relationship becomes linear.

Another important usage is in physics, specifically regarding units. When saying 'meters squared', Persians use متر مربع (metr-e morabba). However, when discussing the numerical operation in a physics formula (like E=mc²), they use مجذور. This distinction is vital: use 'morabba' for units and shapes, use 'majzoor' for the numerical result of an operation.

انرژی با مجذور سرعت نور رابطه مستقیم دارد.
Energy is directly related to the square of the speed of light.

Formal Logic
In formal logic and proofs, 'majzoor' is used to define sets of numbers. For instance, 'the set of all squares of integers'.

آیا مجذور یک عدد گنگ می‌تواند گویا باشد؟
Can the square of an irrational number be rational?

You will encounter مجذور in several specific environments. The most obvious is the educational system. From the moment students in Iran or Afghanistan reach middle school (Grade 6 or 7), this word becomes a staple of their daily vocabulary. Teachers will write it on the chalkboard, and it will appear in every mathematics and physics textbook. If you are watching educational videos on platforms like Aparat (the Persian equivalent of YouTube), you will hear instructors say this word repeatedly during algebra lessons.

Academic Lectures
In university lectures, especially in engineering, physics, and statistics departments, the word is used to describe functions and data transformations. Professors discuss 'majzoorat-e khatā' (squares of errors) when teaching regression.

در این مرحله، باید تفاضل‌ها را به مجذور برسانیم.
At this stage, we must square the differences.

Another place you'll hear it is in scientific documentaries and news reports. When Iranian news agencies (like IRNA or ISNA) report on scientific breakthroughs, nanotechnology, or aerospace achievements, they use formal Persian. If they are describing the intensity of a wave or the force of an impact, they might mention that the value is proportional to the مجذور of another variable. It signals a high level of discourse.

بار وارده با مجذور دهانه ساختمان تغییر می‌کند.
The applied load varies with the square of the building's span.

Standardized Testing
The 'Konkur' (Iran's national university entrance exam) is famous for its difficulty. The word 'majzoor' appears in almost every math and physics question. Students spend years mastering the properties of 'majzoorat' to pass this exam.

کدام گزینه نشان‌دهنده مجذور کامل است؟
Which option represents a perfect square?

You might also encounter it in financial analysis. While less common than 'sood' (profit) or 'ziyan' (loss), analysts looking at volatility (standard deviation) will use the word because the mathematical definition of variance involves squaring the deviations from the mean. If you are listening to a high-level economic podcast in Persian, keep an ear out for this term.

واریانس در واقع میانگین مجذورات انحراف است.
Variance is actually the mean of the squares of deviations.

Software Localization
When using Persian versions of Excel or Google Sheets, the documentation for the 'POWER(number, 2)' function will explain that it calculates the 'majzoor'.

این تابع مجذور ورودی را برمی‌گرداند.
This function returns the square of the input.

The most pervasive mistake learners (and even native speakers) make is confusing مجذور (majzoor) with جذر (jazr). Because they share the same Arabic root, their meanings are often flipped in a moment of confusion. Remember: Jazr is the 'root' (the smaller number you start with), and Majzoor is the 'squared result' (the larger number you end up with). If 4² = 16, then 16 is the مجذور and 4 is the جذر.

Confusing with 'Morabba'
Another common error is using 'majzoor' when referring to a geometric square shape. While related, 'morabba' is the shape, and 'majzoor' is the numerical operation. You cannot say 'I drew a majzoor on the paper'. You must say 'I drew a morabba'.

اشتباه: مجذور عدد ۱۶ برابر ۴ است.
Wrong: The square of 16 is 4. (Correction: The square root of 16 is 4, or the square of 4 is 16).

Mispronunciation is also a minor issue for beginners. The 'z' sound is a zāl (ذ) in spelling, but it is pronounced like a standard English 'z'. Some learners might try to give it a different sound based on Arabic phonetics, but in modern Persian, it's a simple 'z' sound. Also, ensure the 'oo' (vāv) sound is long: maj-zooo-r.

درست: عدد ۱۶ مجذور عدد ۴ است.
Correct: Number 16 is the square of number 4.

Pluralization Errors
Learners often try to use the Persian plural 'majzoor-ha'. While understandable, in mathematical texts, the Arabic plural 'majzoorat' is almost exclusively used. Using 'majzoor-ha' in a thesis might look amateurish.

او مجموع مجذورات را اشتباه حساب کرد.
He calculated the sum of squares incorrectly.

Finally, don't confuse مجذور with مجزّأ (mojazza), which means 'separated' or 'distinct'. They look somewhat similar in script if the diacritics are missing, but their meanings are entirely unrelated. One is about multiplication; the other is about division or separation. Always look for the 'vāv' (و) in مجذور to confirm you are dealing with the mathematical 'square'.

مراقب باشید مجذور را با کلمات مشابه اشتباه نگیرید.
Be careful not to mistake 'square' with similar words.

In Persian, as in English, there are multiple ways to express the concept of squaring a number depending on the level of formality and the specific context. While مجذور is the most technical term, you will often encounter alternatives in conversation and basic schooling.

1. توان دوم (Tavan-e Dovom)
This literally means 'the second power'. It is the most direct alternative and is used very frequently in classrooms. It is slightly less 'heavy' than مجذور. You can say 'do be tavan-e do' (two to the power of two) to get four.

عدد چهار همان توان دوم عدد دو است.
Number four is the same as the second power of number two.

Comparing مجذور and توان دوم: مجذور is a noun (the square), while توان is the concept of 'power' or 'exponent'. You would use مجذور as a result, but توان when describing the process of raising a number.

2. مربع (Morabba)
While 'morabba' primarily means the geometric shape, it is also used in phrases like 'morabba-e kamel' (perfect square). In some older texts or very specific contexts, 'morabba' can be a synonym for 'majzoor', but in modern usage, 'majzoor' is preferred for the number and 'morabba' for the unit or shape.

بیست و پنج یک مربع کامل است.
Twenty-five is a perfect square.

3. ضرب در خود (Zarb dar khod)
This is the informal, descriptive way to say it: 'multiplied by itself'. This is how you would explain the concept to a child or someone who doesn't know the technical terms. It's not a single word, but a functional phrase.

پنج را در خودش ضرب کن تا مجذورش به دست آید.
Multiply five by itself to get its square.

In summary, use مجذور for formal math, توان دوم for general classroom discussion, مربع for shapes and units, and ضرب در خود for simple explanations. Each has its place in the rich tapestry of the Persian language.

Comparison Table
  • Majzoor: Formal, noun, refers to the result (e.g., 49).
  • Tavan-e do: Neutral, refers to the operation (x²).
  • Morabba: Geometric, refers to shape or unit (m²).
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按水平分级的例句

1

مجذور دو، چهار است.

The square of two is four.

Simple subject-complement structure.

2

مجذور سه چند است؟

How much is the square of three?

Interrogative sentence using 'chand'.

3

یک مجذور است.

One is a square.

Basic noun usage.

4

مجذور پنج، بیست و پنج است.

The square of five is twenty-five.

Standard identification.

5

این عدد یک مجذور است.

This number is a square.

Use of demonstrative pronoun 'in'.

6

مجذور چهار را بنویس.

Write the square of four.

Imperative verb 'benevis'.

7

مجذور ده، صد است.

The square of ten is one hundred.

Common math fact.

8

آیا این مجذور است؟

Is this a square?

Yes/No question with 'āyā'.

1

من مجذور عدد شش را می‌دانم.

I know the square of the number six.

Present continuous tense 'midānam'.

2

او مجذور هفت را حساب کرد.

He calculated the square of seven.

Simple past tense 'hesāb kard'.

3

مجذور هشت برابر با شصت و چهار است.

The square of eight is equal to sixty-four.

Use of 'barābar bā' (equal to).

4

ما باید مجذور نه را پیدا کنیم.

We must find the square of nine.

Modal verb 'bāyad' with subjunctive.

5

مجذور این عدد خیلی بزرگ است.

The square of this number is very large.

Use of intensive 'kheyli'.

6

آیا مجذور صفر، صفر است؟

Is the square of zero, zero?

Mathematical logic question.

7

لطفاً مجذور این اعداد را بگویید.

Please say the squares of these numbers.

Polite imperative with 'lotfan'.

8

مجذور یک، همیشه یک است.

The square of one is always one.

Use of adverb 'hamishe'.

1

برای حل این مسئله، مجذور ضلع را به دست آورید.

To solve this problem, obtain the square of the side.

Infinitive phrase for purpose.

2

اگر عددی را به مجذور برسانیم، چه اتفاقی می‌افتد؟

If we raise a number to its square, what happens?

Conditional 'agar' clause.

3

مجذور اعداد منفی همیشه مثبت می‌شود.

The squares of negative numbers always become positive.

General scientific fact.

4

در این فرمول، باید از مجذور سرعت استفاده کرد.

In this formula, the square of the velocity must be used.

Passive-like construction with 'bāyad... kard'.

5

مجذور کامل عددی است که جذر آن صحیح باشد.

A perfect square is a number whose root is an integer.

Relative clause with 'ke'.

6

او مجموع مجذورات را به دقت محاسبه کرد.

He calculated the sum of squares accurately.

Use of Arabic plural 'majzoorat'.

7

رابطه بین این دو متغیر با مجذور یکی از آن‌ها تغییر می‌کند.

The relationship between these two variables changes with the square of one of them.

Complex sentence with prepositional phrases.

8

چگونه می‌توان مجذور یک عدد بزرگ را ذهنی حساب کرد؟

How can one calculate the square of a large number mentally?

Interrogative with 'chegoone' and 'tavānestan'.

1

شدت نور با مجذور فاصله از منبع نسبت عکس دارد.

The intensity of light is inversely proportional to the square of the distance from the source.

Scientific terminology 'nesbat-e aks'.

2

در آمار، مجموع مجذورات خطا برای ارزیابی مدل به کار می‌رود.

In statistics, the sum of squares of error is used to evaluate the model.

Passive voice 'be kār miravad'.

3

با به مجذور رساندن طرفین معادله، مجهول را بیابید.

Find the unknown by squaring both sides of the equation.

Gerund-like 'be... resāndan' construction.

4

مجذور انحراف معیار همان واریانس است.

The square of the standard deviation is the variance.

Equality of two technical terms.

5

او نظریه‌ای بر پایه مجذورات زمان ارائه داد.

He presented a theory based on the squares of time.

Prepositional phrase 'bar pāye-ye'.

6

این تابع ریاضی، مجذور مقادیر ورودی را به خروجی می‌فرستد.

This mathematical function sends the square of the input values to the output.

Technical description of a function.

7

آیا می‌توانید مجذورات این دنباله را تشخیص دهید؟

Can you identify the squares in this sequence?

Ability with 'tavānestan'.

8

تغییرات انرژی جنبشی با مجذور سرعت متناسب است.

Changes in kinetic energy are proportional to the square of velocity.

Physics context.

1

در تحلیل‌های پیشرفته، استفاده از مجذورات وزنی الزامی است.

In advanced analyses, the use of weighted squares is mandatory.

Formal academic tone.

2

الگوریتم مذکور بر مبنای به حداقل رساندن مجذورات خطا عمل می‌کند.

The mentioned algorithm operates based on minimizing the squares of errors.

Use of 'mazkoor' (mentioned) and 'mabnā'.

3

مفهوم مجذور در هندسه تحلیلی کاربردهای گسترده‌ای دارد.

The concept of square has wide applications in analytical geometry.

Abstract subject 'mafhoom'.

4

او با دقت ریاضی، مجذورات پیچیده را در ذهن خود حلاجی کرد.

With mathematical precision, he processed complex squares in his mind.

Literary verb 'hallāji kardan'.

5

تبدیل‌های غیرخطی اغلب شامل به مجذور رساندن متغیرهای مستقل هستند.

Non-linear transformations often involve squaring independent variables.

Subject-verb agreement with complex plural.

6

در متون کهن ریاضی، واژه مجذور به معنای سطح مربع به کار می‌رفت.

In ancient mathematical texts, the word 'majzoor' was used to mean the area of a square.

Historical reference.

7

توزیع کای-دو در واقع توزیع مجموع مجذورات متغیرهای نرمال است.

The Chi-square distribution is actually the distribution of the sum of squares of normal variables.

Highly technical definition.

8

این پژوهش به بررسی تاثیر مجذورات در پایداری سازه می‌پردازد.

This research deals with investigating the impact of squares on structural stability.

Formal research language 'be barresi... mipardāzad'.

1

ظرافت‌های معنایی مجذور در تقابل با مفهوم جذر در فلسفه ریاضی قابل تامل است.

The semantic nuances of 'square' in contrast to the concept of 'root' in the philosophy of mathematics are worth pondering.

Sophisticated vocabulary 'zarāfat-e ma'nāyi'.

2

او در رساله خود، به تبیین جایگاه مجذورات در نظریه اعداد پرداخت.

In his treatise, he proceeded to explain the position of squares in number theory.

Formal verb 'tabyin' (explanation).

3

پارادایم‌های حاکم بر محاسبات مجذورات در قرون وسطی با دوران مدرن متفاوت بود.

The paradigms governing the calculation of squares in the Middle Ages were different from the modern era.

Complex historical comparison.

4

تقلیل مسائل فیزیکی به معادلات مجذورات، گامی بزرگ در علم نوین بود.

Reducing physical problems to equations of squares was a major step in modern science.

Abstract noun 'taghlil' (reduction).

5

دقت در محاسبه مجذورات اعشاری، پیش‌نیاز بسیاری از شبیه‌سازی‌های کامپیوتری است.

Precision in calculating decimal squares is a prerequisite for many computer simulations.

Technical prerequisite 'pish-niyāz'.

6

نوسانات سیستم با مجذورات دامنه تحریک همبستگی مستقیمی نشان می‌دهد.

System fluctuations show a direct correlation with the squares of the excitation amplitude.

Advanced engineering terminology.

7

تحلیل طیفی بر اساس تجزیه مجذورات بسامد صورت می‌گیرد.

Spectral analysis is performed based on the decomposition of frequency squares.

Scientific process description.

8

هرگونه لغزش در فهم مفهوم مجذور می‌تواند به نتایج فاجعه‌باری در مهندسی بینجامد.

Any slip in understanding the concept of square can lead to catastrophic results in engineering.

Strong conditional warning.

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