Class 9 Mathematics - Exploring Algebraic Identities - Visual models of identities Medium Quiz

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वर्गमूल सर्पिल में यदि पिछला कर्ण \(\sqrt{18}\) है, तो (1) इकाई लंब जोड़ने पर नया कर्ण किस गणना से मिलेगा?

In a square root spiral, if the previous hypotenuse is \(\sqrt{18}\), by which calculation will the new hypotenuse be obtained?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{18+1}\)

Step 1

Concept

The correct hypotenuse is (\sqrt{\(\sqrt{18}\)2+12}=\sqrt{19}). In a square root spiral, the number increases by (1) at each step.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{18+1}\). The correct hypotenuse is (\sqrt{\(\sqrt{18}\)2+12}=\sqrt{19}). In a square root spiral, the number increases by (1) at each step.

Step 3

Exam Tip

सही कर्ण (\sqrt{\(\sqrt{18}\)2+12}=\sqrt{19}) होगा। वर्गमूल सर्पिल में हर चरण में संख्या (1) बढ़ती है।

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वर्गमूल सर्पिल में \(\sqrt{288}\) को संख्या रेखा पर रखने से पहले कौन-सा अंतराल पहचानना सही होगा?

Before placing \(\sqrt{288}\) on the number line using a square root spiral, which interval is correct to identify?

Explanation opens after your attempt
Correct Answer

B. \(16<\sqrt{288}<17\)

Step 1

Concept

Because \(16^2<288<17^2\). Therefore \(\sqrt{288}\) lies between (16) and (17).

Step 2

Why this answer is correct

The correct answer is B. \(16<\sqrt{288}<17\). Because \(16^2<288<17^2\). Therefore \(\sqrt{288}\) lies between (16) and (17).

Step 3

Exam Tip

क्योंकि \(16^2<288<17^2\) है। इसलिए \(\sqrt{288}\) (16) और (17) के बीच होगा।

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वर्गमूल सर्पिल में \(\sqrt{28}\) बनाने के लिए कौन-सा पिछला कर्ण और नई लंब भुजा सही है?

To construct \(\sqrt{28}\) in a square root spiral, which previous hypotenuse and new perpendicular side are correct?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{27}\) और (1)\(\sqrt{27}\) and (1)

Step 1

Concept

Since (\(\sqrt{27}\)2+12=28). Therefore \(\sqrt{27}\) is the correct previous hypotenuse.

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{27}\) और (1) / \(\sqrt{27}\) and (1). Since (\(\sqrt{27}\)2+12=28). Therefore \(\sqrt{27}\) is the correct previous hypotenuse.

Step 3

Exam Tip

(\(\sqrt{27}\)2+12=28) होता है। इसलिए पिछले कर्ण के रूप में \(\sqrt{27}\) सही है।

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वर्गमूल सर्पिल में \(\sqrt{323}\) कर्ण पर (1) इकाई लंब बनाई जाए, तो नया कर्ण कौन-सा होगा और उसका सटीक मान क्या होगा?

If a (1) unit perpendicular is drawn on hypotenuse \(\sqrt{323}\) in a square root spiral, what will be the new hypotenuse and its exact value?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{324}\), (18)

Step 1

Concept

The new hypotenuse is \(\sqrt{323+1}=\sqrt{324}\), and \(\sqrt{324}=18\). When a perfect square appears, write the exact whole number.

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{324}\), (18). The new hypotenuse is \(\sqrt{323+1}=\sqrt{324}\), and \(\sqrt{324}=18\). When a perfect square appears, write the exact whole number.

Step 3

Exam Tip

नया कर्ण \(\sqrt{323+1}=\sqrt{324}\) होगा और \(\sqrt{324}=18\) है। पूर्ण वर्ग मिलने पर सटीक पूर्ण संख्या लिखें।

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यदि वर्गमूल सर्पिल में नया कर्ण \(\sqrt{35}\) बनता है, तो उससे ठीक पहले कौन-सा कर्ण होना चाहिए?

If the new hypotenuse \(\sqrt{35}\) is formed in a square root spiral, which hypotenuse should come just before it?

Explanation opens after your attempt
Correct Answer

C. \(\sqrt{34}\)

Step 1

Concept

If the new hypotenuse is \(\sqrt{n+1}\), the previous hypotenuse is \(\sqrt{n}\). Therefore before \(\sqrt{35}\), it is \(\sqrt{34}\).

Step 2

Why this answer is correct

The correct answer is C. \(\sqrt{34}\). If the new hypotenuse is \(\sqrt{n+1}\), the previous hypotenuse is \(\sqrt{n}\). Therefore before \(\sqrt{35}\), it is \(\sqrt{34}\).

Step 3

Exam Tip

नया कर्ण \(\sqrt{n+1}\) हो तो पिछला कर्ण \(\sqrt{n}\) होता है। इसलिए \(\sqrt{35}\) से पहले \(\sqrt{34}\) होगा।

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वर्गमूल सर्पिल में \(\sqrt{45}\) की लंबाई संख्या रेखा पर किस अंतराल में होगी?

In a square root spiral, in which interval will the length \(\sqrt{45}\) lie on the number line?

Explanation opens after your attempt
Correct Answer

B. (6) और (7) के बीचBetween (6) and (7)

Step 1

Concept

Because \(6^2<45<7^2\). Therefore \(\sqrt{45}\) lies between (6) and (7).

Step 2

Why this answer is correct

The correct answer is B. (6) और (7) के बीच / Between (6) and (7). Because \(6^2<45<7^2\). Therefore \(\sqrt{45}\) lies between (6) and (7).

Step 3

Exam Tip

क्योंकि \(6^2<45<7^2\) है। इसलिए \(\sqrt{45}\) (6) और (7) के बीच होगा।

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वर्गमूल सर्पिल में \(\sqrt{99}\) के बाद बनने वाला कर्ण किस प्रकार की संख्या होगा?

In a square root spiral, what type of number will the hypotenuse formed after \(\sqrt{99}\) be?

Explanation opens after your attempt
Correct Answer

A. पूर्ण संख्याWhole number

Step 1

Concept

The next hypotenuse will be \(\sqrt{100}\), and \(\sqrt{100}=10\). Therefore it is a whole number.

Step 2

Why this answer is correct

The correct answer is A. पूर्ण संख्या / Whole number. The next hypotenuse will be \(\sqrt{100}\), and \(\sqrt{100}=10\). Therefore it is a whole number.

Step 3

Exam Tip

अगला कर्ण \(\sqrt{100}\) होगा और \(\sqrt{100}=10\) है। इसलिए वह पूर्ण संख्या है।

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वर्गमूल सर्पिल में \(\sqrt{6}+1=\sqrt{7}\) लिखना क्यों गलत है?

Why is writing \(\sqrt{6}+1=\sqrt{7}\) wrong in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. क्योंकि नया कर्ण (\sqrt{\(\sqrt{6}\)2+12}) से बनता हैBecause the new hypotenuse is formed by (\sqrt{\(\sqrt{6}\)2+12})

Step 1

Concept

In a square root spiral, lengths are not added directly. The correct method is Pythagoras theorem.

Step 2

Why this answer is correct

The correct answer is A. क्योंकि नया कर्ण (\sqrt{\(\sqrt{6}\)2+12}) से बनता है / Because the new hypotenuse is formed by (\sqrt{\(\sqrt{6}\)2+12}). In a square root spiral, lengths are not added directly. The correct method is Pythagoras theorem.

Step 3

Exam Tip

वर्गमूल सर्पिल में सीधे लंबाइयाँ नहीं जोड़ी जातीं। सही तरीका पाइथागोरस प्रमेय है।

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वर्गमूल सर्पिल में \(\sqrt{72}\) और \(\sqrt{81}\) के बारे में कौन-सा कथन सही है?

Which statement about \(\sqrt{72}\) and \(\sqrt{81}\) in a square root spiral is correct?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{72}\) (8) और (9) के बीच है और \(\sqrt{81}=9\) है\(\sqrt{72}\) lies between (8) and (9), and \(\sqrt{81}=9\)

Step 1

Concept

\(8^2<72<9^2\), and \(81=9^2\). Therefore \(\sqrt{81}\) equals (9).

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{72}\) (8) और (9) के बीच है और \(\sqrt{81}=9\) है / \(\sqrt{72}\) lies between (8) and (9), and \(\sqrt{81}=9\). \(8^2<72<9^2\), and \(81=9^2\). Therefore \(\sqrt{81}\) equals (9).

Step 3

Exam Tip

\(8^2<72<9^2\) और \(81=9^2\) है। इसलिए \(\sqrt{81}\) का मान (9) है।

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वर्गमूल सर्पिल में \(\sqrt{120}\) बनाने के लिए किस पिछले कर्ण पर (1) इकाई लंब बनाई जाएगी?

To construct \(\sqrt{120}\) in a square root spiral, on which previous hypotenuse will a (1) unit perpendicular be drawn?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{119}\)

Step 1

Concept

\(\sqrt{120}\) is formed from \(\sqrt{119}\) and a (1) unit perpendicular. The previous hypotenuse number is always (1) less.

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{119}\). \(\sqrt{120}\) is formed from \(\sqrt{119}\) and a (1) unit perpendicular. The previous hypotenuse number is always (1) less.

Step 3

Exam Tip

\(\sqrt{119}\) और (1) इकाई लंब से \(\sqrt{120}\) बनता है। पिछले कर्ण की संख्या हमेशा (1) कम होती है।

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वर्गमूल सर्पिल में \(\sqrt{120}\) संख्या रेखा पर किस अंतराल में होगा?

In a square root spiral, in which interval will \(\sqrt{120}\) lie on the number line?

Explanation opens after your attempt
Correct Answer

B. (10) और (11) के बीचBetween (10) and (11)

Step 1

Concept

Because \(10^2<120<11^2\). Therefore \(\sqrt{120}\) lies between (10) and (11).

Step 2

Why this answer is correct

The correct answer is B. (10) और (11) के बीच / Between (10) and (11). Because \(10^2<120<11^2\). Therefore \(\sqrt{120}\) lies between (10) and (11).

Step 3

Exam Tip

क्योंकि \(10^2<120<11^2\) है। इसलिए \(\sqrt{120}\) (10) और (11) के बीच होगा।

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वर्गमूल सर्पिल में (1) इकाई लंब के स्थान पर (4) इकाई लंब लेने से सामान्य क्रम क्यों टूट जाएगा?

Why will the usual sequence break if a (4) unit perpendicular is used instead of (1) unit in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. क्योंकि \(1^2\) की जगह \(4^2\) जुड़ जाएगाBecause \(4^2\) will be added instead of \(1^2\)

Step 1

Concept

In the usual spiral \(1^2\) is added every time. Taking (4) units adds (16), so the sequence changes.

Step 2

Why this answer is correct

The correct answer is A. क्योंकि \(1^2\) की जगह \(4^2\) जुड़ जाएगा / Because \(4^2\) will be added instead of \(1^2\). In the usual spiral \(1^2\) is added every time. Taking (4) units adds (16), so the sequence changes.

Step 3

Exam Tip

सामान्य सर्पिल में हर बार \(1^2\) जुड़ता है। (4) इकाई लेने पर (16) जुड़ता है और क्रम बदल जाता है।

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वर्गमूल सर्पिल में \(\sqrt{14}\) से \(\sqrt{15}\) बनने का सही कारण कौन-सा है?

What is the correct reason for \(\sqrt{15}\) being formed from \(\sqrt{14}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

C. पिछले कर्ण के वर्ग में \(1^2\) जुड़ता है\(1^2\) is added to the square of the previous hypotenuse

Step 1

Concept

By Pythagoras theorem, (\(\sqrt{14}\)2+12=15). Therefore the new hypotenuse is \(\sqrt{15}\).

Step 2

Why this answer is correct

The correct answer is C. पिछले कर्ण के वर्ग में \(1^2\) जुड़ता है / \(1^2\) is added to the square of the previous hypotenuse. By Pythagoras theorem, (\(\sqrt{14}\)2+12=15). Therefore the new hypotenuse is \(\sqrt{15}\).

Step 3

Exam Tip

पाइथागोरस प्रमेय से (\(\sqrt{14}\)2+12=15) होता है। इसलिए नया कर्ण \(\sqrt{15}\) बनता है।

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वर्गमूल सर्पिल में \(\sqrt{130}\) की सही संख्या-रेखा स्थिति कौन-सी है?

What is the correct number-line position of \(\sqrt{130}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

B. \(11<\sqrt{130}<12\)

Step 1

Concept

Because \(11^2<130<12^2\). Therefore \(\sqrt{130}\) lies between (11) and (12).

Step 2

Why this answer is correct

The correct answer is B. \(11<\sqrt{130}<12\). Because \(11^2<130<12^2\). Therefore \(\sqrt{130}\) lies between (11) and (12).

Step 3

Exam Tip

क्योंकि \(11^2<130<12^2\) है। इसलिए \(\sqrt{130}\) (11) और (12) के बीच है।

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वर्गमूल सर्पिल में \(\sqrt{8}\) बनाने के लिए कौन-सा समकोण त्रिभुज सही है?

Which right triangle is correct for constructing \(\sqrt{8}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{7}\) और (1) भुजाओं वालाWith sides \(\sqrt{7}\) and (1)

Step 1

Concept

(\(\sqrt{7}\)2+12=8). So \(\sqrt{7}\) and (1) are correct to form hypotenuse \(\sqrt{8}\).

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{7}\) और (1) भुजाओं वाला / With sides \(\sqrt{7}\) and (1). (\(\sqrt{7}\)2+12=8). So \(\sqrt{7}\) and (1) are correct to form hypotenuse \(\sqrt{8}\).

Step 3

Exam Tip

(\(\sqrt{7}\)2+12=8) होता है। इसलिए कर्ण \(\sqrt{8}\) बनाने के लिए \(\sqrt{7}\) और (1) सही हैं।

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वर्गमूल सर्पिल में यदि \(\sqrt{48}\) कर्ण पर (1) इकाई लंब बनाई जाए, तो नया कर्ण किस पूर्ण संख्या के बराबर होगा?

If a (1) unit perpendicular is drawn on hypotenuse \(\sqrt{48}\) in a square root spiral, the new hypotenuse will be equal to which whole number?

Explanation opens after your attempt
Correct Answer

B. (7)

Step 1

Concept

The new hypotenuse will be \(\sqrt{49}\), and \(\sqrt{49}=7\). If a perfect square appears, write its exact value.

Step 2

Why this answer is correct

The correct answer is B. (7). The new hypotenuse will be \(\sqrt{49}\), and \(\sqrt{49}=7\). If a perfect square appears, write its exact value.

Step 3

Exam Tip

नया कर्ण \(\sqrt{49}\) होगा और \(\sqrt{49}=7\) है। पूर्ण वर्ग दिखे तो सटीक मान लिखें।

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वर्गमूल सर्पिल में \(\sqrt{26}\) और \(\sqrt{27}\) के बारे में कौन-सा कथन सही है?

Which statement about \(\sqrt{26}\) and \(\sqrt{27}\) in a square root spiral is correct?

Explanation opens after your attempt
Correct Answer

A. दोनों (5) और (6) के बीच हैंBoth are between (5) and (6)

Step 1

Concept

Both \(5^2<26<6^2\) and \(5^2<27<6^2\) are true. Therefore both lie between (5) and (6).

Step 2

Why this answer is correct

The correct answer is A. दोनों (5) और (6) के बीच हैं / Both are between (5) and (6). Both \(5^2<26<6^2\) and \(5^2<27<6^2\) are true. Therefore both lie between (5) and (6).

Step 3

Exam Tip

\(5^2<26<6^2\) और \(5^2<27<6^2\) दोनों सही हैं। इसलिए दोनों (5) और (6) के बीच हैं।

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वर्गमूल सर्पिल में \(\sqrt{143}\) के बाद अगला कर्ण कौन-सा होगा और उसका मान किसके बीच होगा?

In a square root spiral, what will be the next hypotenuse after \(\sqrt{143}\), and between what values will it lie?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{144}\), ठीक (12) पर\(\sqrt{144}\), exactly at (12)

Step 1

Concept

The next hypotenuse is \(\sqrt{144}\), and \(\sqrt{144}=12\). It is not in an interval, but exactly at (12).

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{144}\), ठीक (12) पर / \(\sqrt{144}\), exactly at (12). The next hypotenuse is \(\sqrt{144}\), and \(\sqrt{144}=12\). It is not in an interval, but exactly at (12).

Step 3

Exam Tip

अगला कर्ण \(\sqrt{144}\) है और \(\sqrt{144}=12\) होता है। यह अंतराल में नहीं, ठीक (12) पर है।

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वर्गमूल सर्पिल में कौन-सा उपकरण और उपयोग सही है?

Which tool and use are correct in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. कंपास, कर्ण लंबाई को संख्या रेखा पर स्थानांतरित करने के लिएCompass, to transfer hypotenuse length to the number line

Step 1

Concept

A compass is used to take the hypotenuse length and draw an arc on the number line. This is the correct geometric transfer method.

Step 2

Why this answer is correct

The correct answer is A. कंपास, कर्ण लंबाई को संख्या रेखा पर स्थानांतरित करने के लिए / Compass, to transfer hypotenuse length to the number line. A compass is used to take the hypotenuse length and draw an arc on the number line. This is the correct geometric transfer method.

Step 3

Exam Tip

कंपास से कर्ण की लंबाई लेकर संख्या रेखा पर चाप खींचा जाता है। यह ज्यामितीय स्थानांतरण का सही तरीका है।

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वर्गमूल सर्पिल में \(\sqrt{55}\) किस प्रकार की संख्या है और कहाँ स्थित है?

What type of number is \(\sqrt{55}\) in a square root spiral and where is it located?

Explanation opens after your attempt
Correct Answer

B. अपरिमेय संख्या और (7) तथा (8) के बीचIrrational number and between (7) and (8)

Step 1

Concept

(55) is not a perfect square and \(7^2<55<8^2\). Therefore \(\sqrt{55}\) is irrational and lies between (7) and (8).

Step 2

Why this answer is correct

The correct answer is B. अपरिमेय संख्या और (7) तथा (8) के बीच / Irrational number and between (7) and (8). (55) is not a perfect square and \(7^2<55<8^2\). Therefore \(\sqrt{55}\) is irrational and lies between (7) and (8).

Step 3

Exam Tip

(55) पूर्ण वर्ग नहीं है और \(7^2<55<8^2\) है। इसलिए \(\sqrt{55}\) अपरिमेय है और (7) तथा (8) के बीच है।

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वर्गमूल सर्पिल में \(\sqrt{4}\) तक पहुँचने के लिए कौन-सा क्रम सही है?

Which sequence is correct to reach \(\sqrt{4}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{1}\rightarrow\sqrt{2}\rightarrow\sqrt{3}\rightarrow\sqrt{4}\)

Step 1

Concept

In a square root spiral, hypotenuses are formed in order. In the usual construction, the \(\sqrt{3}\) step is not skipped.

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{1}\rightarrow\sqrt{2}\rightarrow\sqrt{3}\rightarrow\sqrt{4}\). In a square root spiral, hypotenuses are formed in order. In the usual construction, the \(\sqrt{3}\) step is not skipped.

Step 3

Exam Tip

वर्गमूल सर्पिल में कर्ण क्रम से बनते हैं। सामान्य निर्माण में \(\sqrt{3}\) चरण छोड़ा नहीं जाता।

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वर्गमूल सर्पिल में \(\sqrt{2}\) और \(\sqrt{3}\) बनने की प्रक्रिया में समानता क्या है?

What is common in the formation process of \(\sqrt{2}\) and \(\sqrt{3}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. दोनों में समकोण त्रिभुज और पाइथागोरस प्रमेय का उपयोग होता हैBoth use a right triangle and Pythagoras theorem

Step 1

Concept

Both constructions are based on right triangles. The hypotenuse is found by Pythagoras theorem.

Step 2

Why this answer is correct

The correct answer is A. दोनों में समकोण त्रिभुज और पाइथागोरस प्रमेय का उपयोग होता है / Both use a right triangle and Pythagoras theorem. Both constructions are based on right triangles. The hypotenuse is found by Pythagoras theorem.

Step 3

Exam Tip

दोनों निर्माण समकोण त्रिभुज पर आधारित हैं। कर्ण पाइथागोरस प्रमेय से निकाला जाता है।

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वर्गमूल सर्पिल में \(\sqrt{200}\) संख्या रेखा पर किस अंतराल में आएगा?

In a square root spiral, in which interval will \(\sqrt{200}\) lie on the number line?

Explanation opens after your attempt
Correct Answer

C. (14) और (15) के बीचBetween (14) and (15)

Step 1

Concept

Because \(14^2<200<15^2\). Therefore \(\sqrt{200}\) lies between (14) and (15).

Step 2

Why this answer is correct

The correct answer is C. (14) और (15) के बीच / Between (14) and (15). Because \(14^2<200<15^2\). Therefore \(\sqrt{200}\) lies between (14) and (15).

Step 3

Exam Tip

क्योंकि \(14^2<200<15^2\) है। इसलिए \(\sqrt{200}\) (14) और (15) के बीच होगा।

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वर्गमूल सर्पिल में \(\sqrt{15}\) बनाने के बाद अगला कर्ण किस प्रकार की संख्या होगा?

After constructing \(\sqrt{15}\) in a square root spiral, what type of number will the next hypotenuse be?

Explanation opens after your attempt
Correct Answer

A. पूर्ण संख्याWhole number

Step 1

Concept

The next hypotenuse will be \(\sqrt{16}\), and \(\sqrt{16}=4\). Therefore it is a whole number.

Step 2

Why this answer is correct

The correct answer is A. पूर्ण संख्या / Whole number. The next hypotenuse will be \(\sqrt{16}\), and \(\sqrt{16}=4\). Therefore it is a whole number.

Step 3

Exam Tip

अगला कर्ण \(\sqrt{16}\) होगा और \(\sqrt{16}=4\) है। इसलिए वह पूर्ण संख्या है।

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वर्गमूल सर्पिल में \(\sqrt{101}\) और \(\sqrt{121}\) के बारे में कौन-सा कथन सही है?

Which statement about \(\sqrt{101}\) and \(\sqrt{121}\) in a square root spiral is correct?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{101}\) (10) और (11) के बीच है और \(\sqrt{121}=11\) है\(\sqrt{101}\) is between (10) and (11), and \(\sqrt{121}=11\)

Step 1

Concept

\(10^2<101<11^2\), and \(121=11^2\). Therefore \(\sqrt{121}=11\).

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{101}\) (10) और (11) के बीच है और \(\sqrt{121}=11\) है / \(\sqrt{101}\) is between (10) and (11), and \(\sqrt{121}=11\). \(10^2<101<11^2\), and \(121=11^2\). Therefore \(\sqrt{121}=11\).

Step 3

Exam Tip

\(10^2<101<11^2\) और \(121=11^2\) है। इसलिए \(\sqrt{121}=11\) है।

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वर्गमूल सर्पिल में \(\sqrt{60}\) बनाने के लिए सही पाइथागोरस समीकरण कौन-सा है?

Which Pythagoras equation is correct for constructing \(\sqrt{60}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. (\(\sqrt{59}\)2+12=60)

Step 1

Concept

\(\sqrt{59}\) is the previous hypotenuse and the new perpendicular is (1) unit. Therefore the new hypotenuse is \(\sqrt{60}\).

Step 2

Why this answer is correct

The correct answer is A. (\(\sqrt{59}\)2+12=60). \(\sqrt{59}\) is the previous hypotenuse and the new perpendicular is (1) unit. Therefore the new hypotenuse is \(\sqrt{60}\).

Step 3

Exam Tip

\(\sqrt{59}\) पिछले कर्ण की लंबाई है और नई लंब (1) इकाई है। इसलिए नया कर्ण \(\sqrt{60}\) होगा।

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वर्गमूल सर्पिल में यदि \(\sqrt{n}\) पूर्ण संख्या है, तो (n) के बारे में सही निष्कर्ष क्या है?

If \(\sqrt{n}\) is a whole number in a square root spiral, what is the correct conclusion about (n)?

Explanation opens after your attempt
Correct Answer

A. (n) पूर्ण वर्ग है(n) is a perfect square

Step 1

Concept

A whole number square root is obtained only when (n) is a perfect square. For example, \(\sqrt{81}=9\).

Step 2

Why this answer is correct

The correct answer is A. (n) पूर्ण वर्ग है / (n) is a perfect square. A whole number square root is obtained only when (n) is a perfect square. For example, \(\sqrt{81}=9\).

Step 3

Exam Tip

पूर्ण संख्या वर्गमूल तभी मिलता है जब (n) पूर्ण वर्ग हो। जैसे \(\sqrt{81}=9\)।

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वर्गमूल सर्पिल में \(\sqrt{242}\) किस अंतराल में होगा?

In a square root spiral, in which interval will \(\sqrt{242}\) lie?

Explanation opens after your attempt
Correct Answer

B. (15) और (16) के बीचBetween (15) and (16)

Step 1

Concept

Because \(15^2<242<16^2\). Therefore \(\sqrt{242}\) lies between (15) and (16).

Step 2

Why this answer is correct

The correct answer is B. (15) और (16) के बीच / Between (15) and (16). Because \(15^2<242<16^2\). Therefore \(\sqrt{242}\) lies between (15) and (16).

Step 3

Exam Tip

क्योंकि \(15^2<242<16^2\) है। इसलिए \(\sqrt{242}\) (15) और (16) के बीच होगा।

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वर्गमूल सर्पिल में \(\sqrt{3}\) से \(\sqrt{4}\) बनने पर कौन-सा कथन सही है?

When \(\sqrt{4}\) is formed from \(\sqrt{3}\) in a square root spiral, which statement is correct?

Explanation opens after your attempt
Correct Answer

B. (\(\sqrt{3}\)2+12=4) इसलिए कर्ण \(\sqrt{4}\) है(\(\sqrt{3}\)2+12=4), so the hypotenuse is \(\sqrt{4}\)

Step 1

Concept

In a square root spiral, the sum of squares is taken by Pythagoras theorem. Directly adding lengths is wrong.

Step 2

Why this answer is correct

The correct answer is B. (\(\sqrt{3}\)2+12=4) इसलिए कर्ण \(\sqrt{4}\) है / (\(\sqrt{3}\)2+12=4), so the hypotenuse is \(\sqrt{4}\). In a square root spiral, the sum of squares is taken by Pythagoras theorem. Directly adding lengths is wrong.

Step 3

Exam Tip

वर्गमूल सर्पिल में पाइथागोरस प्रमेय से वर्गों का योग लिया जाता है। सीधे लंबाइयाँ जोड़ना गलत है।

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वर्गमूल सर्पिल में \(\sqrt{224}\) के बाद अगला कर्ण क्या होगा और उसका सटीक मान क्या है?

In a square root spiral, what will be the next hypotenuse after \(\sqrt{224}\), and what is its exact value?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{225}\), (15)

Step 1

Concept

The next hypotenuse is \(\sqrt{225}\), and \(\sqrt{225}=15\). Recognizing perfect squares is important.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{225}\), (15). The next hypotenuse is \(\sqrt{225}\), and \(\sqrt{225}=15\). Recognizing perfect squares is important.

Step 3

Exam Tip

अगला कर्ण \(\sqrt{225}\) है और \(\sqrt{225}=15\) होता है। पूर्ण वर्ग पहचानना जरूरी है।

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वर्गमूल सर्पिल में \(\sqrt{2}\) और \(\sqrt{8}\) के प्रकार के बारे में सही कथन कौन-सा है?

Which statement about the type of \(\sqrt{2}\) and \(\sqrt{8}\) in a square root spiral is correct?

Explanation opens after your attempt
Correct Answer

B. दोनों अपरिमेय संख्याएँ हैंBoth are irrational numbers

Step 1

Concept

The numbers (2) and (8) are not perfect squares. Therefore both square roots are irrational.

Step 2

Why this answer is correct

The correct answer is B. दोनों अपरिमेय संख्याएँ हैं / Both are irrational numbers. The numbers (2) and (8) are not perfect squares. Therefore both square roots are irrational.

Step 3

Exam Tip

(2) और (8) पूर्ण वर्ग नहीं हैं। इसलिए दोनों के वर्गमूल अपरिमेय हैं।

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वर्गमूल सर्पिल में \(\sqrt{150}\) संख्या रेखा पर कहाँ होगा?

Where will \(\sqrt{150}\) lie on the number line in a square root spiral?

Explanation opens after your attempt
Correct Answer

B. (12) और (13) के बीचBetween (12) and (13)

Step 1

Concept

Because \(12^2<150<13^2\). Therefore \(\sqrt{150}\) lies between (12) and (13).

Step 2

Why this answer is correct

The correct answer is B. (12) और (13) के बीच / Between (12) and (13). Because \(12^2<150<13^2\). Therefore \(\sqrt{150}\) lies between (12) and (13).

Step 3

Exam Tip

क्योंकि \(12^2<150<13^2\) है। इसलिए \(\sqrt{150}\) (12) और (13) के बीच होगा।

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वर्गमूल सर्पिल में \(\sqrt{5}\) बनाने के लिए कौन-सी भुजा-जोड़ी सही है?

Which side pair is correct for constructing \(\sqrt{5}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{4}\) और (1)\(\sqrt{4}\) and (1)

Step 1

Concept

(\(\sqrt{4}\)2+12=5). Therefore sides \(\sqrt{4}\) and (1) form hypotenuse \(\sqrt{5}\).

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{4}\) और (1) / \(\sqrt{4}\) and (1). (\(\sqrt{4}\)2+12=5). Therefore sides \(\sqrt{4}\) and (1) form hypotenuse \(\sqrt{5}\).

Step 3

Exam Tip

(\(\sqrt{4}\)2+12=5) है। इसलिए \(\sqrt{4}\) और (1) से कर्ण \(\sqrt{5}\) बनेगा।

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वर्गमूल सर्पिल में \(\sqrt{168}\) का सही अंतराल कौन-सा है?

What is the correct interval for \(\sqrt{168}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

B. \(12<\sqrt{168}<13\)

Step 1

Concept

Because \(12^2<168<13^2\). Therefore \(\sqrt{168}\) lies between (12) and (13).

Step 2

Why this answer is correct

The correct answer is B. \(12<\sqrt{168}<13\). Because \(12^2<168<13^2\). Therefore \(\sqrt{168}\) lies between (12) and (13).

Step 3

Exam Tip

क्योंकि \(12^2<168<13^2\) है। इसलिए \(\sqrt{168}\) (12) और (13) के बीच है।

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वर्गमूल सर्पिल में \(\sqrt{63}\) बनाने के बाद अगला कर्ण कौन-सा होगा और वह किस संख्या के बराबर होगा?

After constructing \(\sqrt{63}\) in a square root spiral, what will be the next hypotenuse and which number will it equal?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{64}\), (8)

Step 1

Concept

The next hypotenuse will be \(\sqrt{64}\), and \(\sqrt{64}=8\). At a perfect square, an exact whole number is obtained.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{64}\), (8). The next hypotenuse will be \(\sqrt{64}\), and \(\sqrt{64}=8\). At a perfect square, an exact whole number is obtained.

Step 3

Exam Tip

अगला कर्ण \(\sqrt{64}\) होगा और \(\sqrt{64}=8\) है। पूर्ण वर्ग पर सटीक पूर्ण संख्या मिलती है।

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वर्गमूल सर्पिल में \(\sqrt{90}\) और \(\sqrt{100}\) की तुलना में सही कथन कौन-सा है?

Which statement is correct when comparing \(\sqrt{90}\) and \(\sqrt{100}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{90}\) (9) और (10) के बीच है और \(\sqrt{100}=10\) है\(\sqrt{90}\) is between (9) and (10), and \(\sqrt{100}=10\)

Step 1

Concept

\(9^2<90<10^2\), and \(100=10^2\). Therefore the first statement is correct.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{90}\) (9) और (10) के बीच है और \(\sqrt{100}=10\) है / \(\sqrt{90}\) is between (9) and (10), and \(\sqrt{100}=10\). \(9^2<90<10^2\), and \(100=10^2\). Therefore the first statement is correct.

Step 3

Exam Tip

\(9^2<90<10^2\) और \(100=10^2\) है। इसलिए तुलना में पहला कथन सही है।

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वर्गमूल सर्पिल में (1) इकाई लंब और \(90^\circ\) कोण दोनों का संयुक्त महत्व क्या है?

What is the combined importance of the (1) unit perpendicular and \(90^\circ\) angle in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. इनसे (\(\sqrt{n}\)2+12=n+1) लागू होता हैThey allow (\(\sqrt{n}\)2+12=n+1) to apply

Step 1

Concept

The (1) unit perpendicular and right angle allow Pythagoras theorem to apply correctly. This forms successive square roots.

Step 2

Why this answer is correct

The correct answer is A. इनसे (\(\sqrt{n}\)2+12=n+1) लागू होता है / They allow (\(\sqrt{n}\)2+12=n+1) to apply. The (1) unit perpendicular and right angle allow Pythagoras theorem to apply correctly. This forms successive square roots.

Step 3

Exam Tip

(1) इकाई लंब और समकोण से पाइथागोरस प्रमेय सही लागू होता है। इसी से क्रमिक वर्गमूल बनते हैं।

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वर्गमूल सर्पिल में \(\sqrt{195}\) किस अंतराल में होगा?

In a square root spiral, in which interval will \(\sqrt{195}\) lie?

Explanation opens after your attempt
Correct Answer

B. (13) और (14) के बीचBetween (13) and (14)

Step 1

Concept

Because \(13^2<195<14^2\). Therefore \(\sqrt{195}\) lies between (13) and (14).

Step 2

Why this answer is correct

The correct answer is B. (13) और (14) के बीच / Between (13) and (14). Because \(13^2<195<14^2\). Therefore \(\sqrt{195}\) lies between (13) and (14).

Step 3

Exam Tip

क्योंकि \(13^2<195<14^2\) है। इसलिए \(\sqrt{195}\) (13) और (14) के बीच होगा।

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वर्गमूल सर्पिल में कौन-सा कथन सबसे गलत विधि दिखाता है?

Which statement shows the most incorrect method for a square root spiral?

Explanation opens after your attempt
Correct Answer

D. अगला कर्ण पिछले कर्ण में सीधे (1) जोड़कर निकालनाFinding the next hypotenuse by directly adding (1) to the previous hypotenuse

Step 1

Concept

Direct addition is not used in a square root spiral. The new hypotenuse is obtained from a right triangle and Pythagoras theorem.

Step 2

Why this answer is correct

The correct answer is D. अगला कर्ण पिछले कर्ण में सीधे (1) जोड़कर निकालना / Finding the next hypotenuse by directly adding (1) to the previous hypotenuse. Direct addition is not used in a square root spiral. The new hypotenuse is obtained from a right triangle and Pythagoras theorem.

Step 3

Exam Tip

वर्गमूल सर्पिल में सीधे जोड़ नहीं किया जाता। नया कर्ण समकोण त्रिभुज और पाइथागोरस प्रमेय से मिलता है।

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वर्गमूल सर्पिल में \(\sqrt{224}\) बनाने के लिए कौन-सा पिछला कर्ण सही है?

Which previous hypotenuse is correct for constructing \(\sqrt{224}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{223}\)

Step 1

Concept

Adding a (1) unit perpendicular to \(\sqrt{223}\) forms \(\sqrt{224}\). The number increases by (1) in the next hypotenuse.

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{223}\). Adding a (1) unit perpendicular to \(\sqrt{223}\) forms \(\sqrt{224}\). The number increases by (1) in the next hypotenuse.

Step 3

Exam Tip

\(\sqrt{223}\) में (1) इकाई लंब जोड़ने पर \(\sqrt{224}\) बनता है। अगले कर्ण में संख्या (1) बढ़ती है।

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वर्गमूल सर्पिल में \(\sqrt{2}\) की लंबाई को संख्या रेखा पर सही रखने की प्रक्रिया कौन-सी है?

What is the correct process to place the length \(\sqrt{2}\) on the number line using a square root spiral?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{2}\) कर्ण की लंबाई कंपास में लेकर मूल बिंदु से चाप खींचनाTake the \(\sqrt{2}\) hypotenuse length in a compass and draw an arc from the origin

Step 1

Concept

The hypotenuse length of the square root to be marked is taken in the compass. Drawing an arc from the origin is the correct way.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{2}\) कर्ण की लंबाई कंपास में लेकर मूल बिंदु से चाप खींचना / Take the \(\sqrt{2}\) hypotenuse length in a compass and draw an arc from the origin. The hypotenuse length of the square root to be marked is taken in the compass. Drawing an arc from the origin is the correct way.

Step 3

Exam Tip

जिस वर्गमूल को अंकित करना है, उसी कर्ण की लंबाई कंपास में ली जाती है। मूल बिंदु से चाप खींचना सही तरीका है।

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वर्गमूल सर्पिल में \(\sqrt{252}\) किस दो पूर्ण संख्याओं के बीच होगा?

In a square root spiral, \(\sqrt{252}\) will lie between which two whole numbers?

Explanation opens after your attempt
Correct Answer

B. (15) और (16)(15) and (16)

Step 1

Concept

Because \(15^2<252<16^2\). Therefore \(\sqrt{252}\) lies between (15) and (16).

Step 2

Why this answer is correct

The correct answer is B. (15) और (16) / (15) and (16). Because \(15^2<252<16^2\). Therefore \(\sqrt{252}\) lies between (15) and (16).

Step 3

Exam Tip

क्योंकि \(15^2<252<16^2\) है। इसलिए \(\sqrt{252}\) (15) और (16) के बीच होगा।

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वर्गमूल सर्पिल में यदि \(\sqrt{n+1}\) नया कर्ण है, तो सही निर्माण संबंध कौन-सा है?

If \(\sqrt{n+1}\) is the new hypotenuse in a square root spiral, which construction relation is correct?

Explanation opens after your attempt
Correct Answer

A. पिछला कर्ण \(\sqrt{n}\) और नई लंब (1) इकाईPrevious hypotenuse \(\sqrt{n}\) and new perpendicular (1) unit

Step 1

Concept

Because (\(\sqrt{n}\)2+12=n+1). Therefore the new hypotenuse becomes \(\sqrt{n+1}\).

Step 2

Why this answer is correct

The correct answer is A. पिछला कर्ण \(\sqrt{n}\) और नई लंब (1) इकाई / Previous hypotenuse \(\sqrt{n}\) and new perpendicular (1) unit. Because (\(\sqrt{n}\)2+12=n+1). Therefore the new hypotenuse becomes \(\sqrt{n+1}\).

Step 3

Exam Tip

क्योंकि (\(\sqrt{n}\)2+12=n+1) होता है। इसलिए नया कर्ण \(\sqrt{n+1}\) बनता है।

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वर्गमूल सर्पिल में \(\sqrt{24}\) और \(\sqrt{25}\) के बारे में सही कथन क्या है?

What is the correct statement about \(\sqrt{24}\) and \(\sqrt{25}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{24}\) (4) और (5) के बीच है और \(\sqrt{25}=5\) है\(\sqrt{24}\) is between (4) and (5), and \(\sqrt{25}=5\)

Step 1

Concept

\(4^2<24<5^2\), and \(25=5^2\). Therefore the exact value of \(\sqrt{25}\) is (5).

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{24}\) (4) और (5) के बीच है और \(\sqrt{25}=5\) है / \(\sqrt{24}\) is between (4) and (5), and \(\sqrt{25}=5\). \(4^2<24<5^2\), and \(25=5^2\). Therefore the exact value of \(\sqrt{25}\) is (5).

Step 3

Exam Tip

\(4^2<24<5^2\) और \(25=5^2\) है। इसलिए \(\sqrt{25}\) का सटीक मान (5) है।

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वर्गमूल सर्पिल में \(\sqrt{300}\) का सही संख्या-रेखा अंतराल कौन-सा है?

What is the correct number-line interval for \(\sqrt{300}\) in a square root spiral?

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Correct Answer

C. (17) और (18) के बीचBetween (17) and (18)

Step 1

Concept

Because \(17^2<300<18^2\). Therefore \(\sqrt{300}\) lies between (17) and (18).

Step 2

Why this answer is correct

The correct answer is C. (17) और (18) के बीच / Between (17) and (18). Because \(17^2<300<18^2\). Therefore \(\sqrt{300}\) lies between (17) and (18).

Step 3

Exam Tip

क्योंकि \(17^2<300<18^2\) है। इसलिए \(\sqrt{300}\) (17) और (18) के बीच होगा।

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वर्गमूल सर्पिल में \(\sqrt{15}\) से \(\sqrt{16}\) बनने पर क्या विशेष बात होती है?

What special thing happens when \(\sqrt{16}\) is formed from \(\sqrt{15}\) in a square root spiral?

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Correct Answer

A. नया कर्ण पूर्ण संख्या (4) बन जाता हैThe new hypotenuse becomes the whole number (4)

Step 1

Concept

\(\sqrt{16}=4\). When the number is a perfect square, the square root becomes a whole number.

Step 2

Why this answer is correct

The correct answer is A. नया कर्ण पूर्ण संख्या (4) बन जाता है / The new hypotenuse becomes the whole number (4). \(\sqrt{16}=4\). When the number is a perfect square, the square root becomes a whole number.

Step 3

Exam Tip

\(\sqrt{16}=4\) है। जब संख्या पूर्ण वर्ग हो, तो वर्गमूल पूर्ण संख्या बनता है।

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वर्गमूल सर्पिल में \(\sqrt{110}\) बनाने के लिए कौन-सा पिछला कर्ण और नई लंब सही है?

To construct \(\sqrt{110}\) in a square root spiral, which previous hypotenuse and new perpendicular are correct?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{109}\) और (1)\(\sqrt{109}\) and (1)

Step 1

Concept

Since (\(\sqrt{109}\)2+12=110). Therefore \(\sqrt{109}\) is the correct previous hypotenuse.

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{109}\) और (1) / \(\sqrt{109}\) and (1). Since (\(\sqrt{109}\)2+12=110). Therefore \(\sqrt{109}\) is the correct previous hypotenuse.

Step 3

Exam Tip

(\(\sqrt{109}\)2+12=110) होता है। इसलिए पिछले कर्ण के रूप में \(\sqrt{109}\) सही है।

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वर्गमूल सर्पिल में यदि \(\sqrt{80}\) कर्ण पर (1) इकाई लंब बनाई जाए, तो नया कर्ण किस अंतराल में होगा?

If a (1) unit perpendicular is drawn on hypotenuse \(\sqrt{80}\) in a square root spiral, in which interval will the new hypotenuse lie?

Explanation opens after your attempt
Correct Answer

C. ठीक (9) परExactly at (9)

Step 1

Concept

The new hypotenuse will be \(\sqrt{81}\), and \(\sqrt{81}=9\). Therefore it lies exactly at (9).

Step 2

Why this answer is correct

The correct answer is C. ठीक (9) पर / Exactly at (9). The new hypotenuse will be \(\sqrt{81}\), and \(\sqrt{81}=9\). Therefore it lies exactly at (9).

Step 3

Exam Tip

नया कर्ण \(\sqrt{81}\) होगा और \(\sqrt{81}=9\) है। इसलिए वह ठीक (9) पर स्थित होगा।

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वर्गमूल सर्पिल में \(\sqrt{2}\) से \(\sqrt{5}\) तक पहुँचने का सही क्रम कौन-सा है?

What is the correct order to reach from \(\sqrt{2}\) to \(\sqrt{5}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{2}\rightarrow\sqrt{3}\rightarrow\sqrt{4}\rightarrow\sqrt{5}\)

Step 1

Concept

In a square root spiral, hypotenuses are formed successively. In the usual construction, intermediate steps are not skipped.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{2}\rightarrow\sqrt{3}\rightarrow\sqrt{4}\rightarrow\sqrt{5}\). In a square root spiral, hypotenuses are formed successively. In the usual construction, intermediate steps are not skipped.

Step 3

Exam Tip

वर्गमूल सर्पिल में कर्ण क्रमिक रूप से बनते हैं। सामान्य निर्माण में बीच के चरण छोड़े नहीं जाते।

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वर्गमूल सर्पिल में कौन-सा कथन माध्यम स्तर पर सबसे सटीक है?

Which statement is most precise at medium level for a square root spiral?

Explanation opens after your attempt
Correct Answer

A. यह समकोण त्रिभुजों की श्रृंखला है, जहाँ पिछला कर्ण और (1) इकाई लंब अगला वर्गमूल बनाते हैंIt is a chain of right triangles where the previous hypotenuse and (1) unit perpendicular form the next square root

Step 1

Concept

A square root spiral is a stepwise construction based on Pythagoras theorem. Each new hypotenuse gives the next square root.

Step 2

Why this answer is correct

The correct answer is A. यह समकोण त्रिभुजों की श्रृंखला है, जहाँ पिछला कर्ण और (1) इकाई लंब अगला वर्गमूल बनाते हैं / It is a chain of right triangles where the previous hypotenuse and (1) unit perpendicular form the next square root. A square root spiral is a stepwise construction based on Pythagoras theorem. Each new hypotenuse gives the next square root.

Step 3

Exam Tip

वर्गमूल सर्पिल पाइथागोरस प्रमेय पर आधारित क्रमिक निर्माण है। हर नया कर्ण अगला वर्गमूल देता है।

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