Class 9 Mathematics - Number Systems - Square root spiral Easy Quiz

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वर्गमूल सर्पिल में सबसे पहले कौन-सा रेखाखंड बनाया जाता है?

Which line segment is drawn first in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. (1) इकाई का रेखाखंडA line segment of (1) unit

Step 1

Concept

The construction starts with a (1) unit line segment. The first right triangle is made from it.

Step 2

Why this answer is correct

The correct answer is A. (1) इकाई का रेखाखंड / A line segment of (1) unit. The construction starts with a (1) unit line segment. The first right triangle is made from it.

Step 3

Exam Tip

शुरुआत (1) इकाई के रेखाखंड से होती है। इसी से पहला समकोण त्रिभुज बनाया जाता है।

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वर्गमूल सर्पिल में (1) इकाई और (1) इकाई भुजाओं से बने समकोण त्रिभुज का कर्ण क्या होगा?

In a square root spiral, what is the hypotenuse of a right triangle with sides (1) unit and (1) unit?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{2}\)

Step 1

Concept

By Pythagoras theorem the hypotenuse is \(\sqrt{1^2+1^2}=\sqrt{2}\). The first main hypotenuse is \(\sqrt{2}\).

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{2}\). By Pythagoras theorem the hypotenuse is \(\sqrt{1^2+1^2}=\sqrt{2}\). The first main hypotenuse is \(\sqrt{2}\).

Step 3

Exam Tip

पाइथागोरस प्रमेय से कर्ण \(\sqrt{1^2+1^2}=\sqrt{2}\) होता है। पहला मुख्य कर्ण \(\sqrt{2}\) है।

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वर्गमूल सर्पिल में प्रत्येक नए त्रिभुज की नई लंब भुजा कितनी रखी जाती है?

In a square root spiral, what is the length of the new perpendicular side in each new triangle?

Explanation opens after your attempt
Correct Answer

B. (1) इकाई(1) unit

Step 1

Concept

At every step the new perpendicular side is kept (1) unit. This forms the next square root.

Step 2

Why this answer is correct

The correct answer is B. (1) इकाई / (1) unit. At every step the new perpendicular side is kept (1) unit. This forms the next square root.

Step 3

Exam Tip

हर चरण में नई लंब भुजा (1) इकाई रखी जाती है। इसी से अगला वर्गमूल बनता है।

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वर्गमूल सर्पिल में समकोण त्रिभुज का कर्ण निकालने के लिए कौन-सा प्रमेय उपयोग होता है?

Which theorem is used to find the hypotenuse of a right triangle in a square root spiral?

Explanation opens after your attempt
Correct Answer

C. पाइथागोरस प्रमेयPythagoras theorem

Step 1

Concept

Pythagoras theorem is used to find the hypotenuse. So recognizing the right triangle is important.

Step 2

Why this answer is correct

The correct answer is C. पाइथागोरस प्रमेय / Pythagoras theorem. Pythagoras theorem is used to find the hypotenuse. So recognizing the right triangle is important.

Step 3

Exam Tip

कर्ण ज्ञात करने के लिए पाइथागोरस प्रमेय लगाया जाता है। इसलिए समकोण त्रिभुज पहचानना जरूरी है।

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\(\sqrt{2}\) कर्ण पर (1) इकाई लंब जोड़ने पर अगला कर्ण क्या बनेगा?

What will be the next hypotenuse after adding a (1) unit perpendicular to the hypotenuse \(\sqrt{2}\)?

Explanation opens after your attempt
Correct Answer

D. \(\sqrt{3}\)

Step 1

Concept

The new hypotenuse is (\sqrt{\(\sqrt{2}\)2+12}=\sqrt{3}). Each time (1) is added to the number.

Step 2

Why this answer is correct

The correct answer is D. \(\sqrt{3}\). The new hypotenuse is (\sqrt{\(\sqrt{2}\)2+12}=\sqrt{3}). Each time (1) is added to the number.

Step 3

Exam Tip

नया कर्ण (\sqrt{\(\sqrt{2}\)2+12}=\sqrt{3}) होगा। हर बार संख्या में (1) जुड़ता है।

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\(\sqrt{3}\) के बाद वर्गमूल सर्पिल में अगला कर्ण कौन-सा होगा?

After \(\sqrt{3}\), which hypotenuse comes next in a square root spiral?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{4}\)

Step 1

Concept

With \(\sqrt{3}\) and a (1) unit perpendicular the new hypotenuse is \(\sqrt{4}\). Take the next square root in sequence.

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{4}\). With \(\sqrt{3}\) and a (1) unit perpendicular the new hypotenuse is \(\sqrt{4}\). Take the next square root in sequence.

Step 3

Exam Tip

\(\sqrt{3}\) के साथ (1) इकाई लंब से नया कर्ण \(\sqrt{4}\) बनता है। क्रम में अगला वर्गमूल लें।

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वर्गमूल सर्पिल में कर्णों का सही प्रारंभिक क्रम कौन-सा है?

What is the correct initial sequence of hypotenuses in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{1},\sqrt{2},\sqrt{3},\sqrt{4}\)

Step 1

Concept

The hypotenuses progress as \(\sqrt{1},\sqrt{2},\sqrt{3}\) and so on. In the spiral the number increases by one.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{1},\sqrt{2},\sqrt{3},\sqrt{4}\). The hypotenuses progress as \(\sqrt{1},\sqrt{2},\sqrt{3}\) and so on. In the spiral the number increases by one.

Step 3

Exam Tip

कर्ण क्रम से \(\sqrt{1},\sqrt{2},\sqrt{3}\) आगे बढ़ते हैं। सर्पिल में संख्या एक-एक बढ़ती है।

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यदि पिछले कर्ण की लंबाई \(\sqrt{8}\) है, तो (1) इकाई लंब जोड़ने पर नया कर्ण क्या होगा?

If the previous hypotenuse is \(\sqrt{8}\), what is the new hypotenuse after adding a (1) unit perpendicular?

Explanation opens after your attempt
Correct Answer

C. \(\sqrt{9}\)

Step 1

Concept

The new hypotenuse is \(\sqrt{8+1}=\sqrt{9}\). This is the simple rule of the square root spiral.

Step 2

Why this answer is correct

The correct answer is C. \(\sqrt{9}\). The new hypotenuse is \(\sqrt{8+1}=\sqrt{9}\). This is the simple rule of the square root spiral.

Step 3

Exam Tip

नया कर्ण \(\sqrt{8+1}=\sqrt{9}\) होगा। यह वर्गमूल सर्पिल का सरल नियम है।

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वर्गमूल सर्पिल में \(\sqrt{12}\) बनाने के लिए पिछला कर्ण कौन-सा होना चाहिए?

To make \(\sqrt{12}\) in a square root spiral, what should be the previous hypotenuse?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{11}\)

Step 1

Concept

Adding a (1) unit perpendicular to \(\sqrt{11}\) gives \(\sqrt{12}\). The previous hypotenuse has one less number.

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{11}\). Adding a (1) unit perpendicular to \(\sqrt{11}\) gives \(\sqrt{12}\). The previous hypotenuse has one less number.

Step 3

Exam Tip

\(\sqrt{11}\) पर (1) इकाई लंब जोड़ने से \(\sqrt{12}\) बनता है। पिछला कर्ण एक कम संख्या का होता है।

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वर्गमूल सर्पिल में \(\sqrt{16}\) किस संख्या के बराबर है?

In a square root spiral, \(\sqrt{16}\) is equal to which number?

Explanation opens after your attempt
Correct Answer

C. (4)

Step 1

Concept

\(\sqrt{16}=4\). Square roots of perfect squares give whole numbers.

Step 2

Why this answer is correct

The correct answer is C. (4). \(\sqrt{16}=4\). Square roots of perfect squares give whole numbers.

Step 3

Exam Tip

\(\sqrt{16}=4\) होता है। पूर्ण वर्गों के वर्गमूल पूर्ण संख्याएँ देते हैं।

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वर्गमूल सर्पिल में \(\sqrt{5}\) किस प्रकार की संख्या है?

In a square root spiral, what type of number is \(\sqrt{5}\)?

Explanation opens after your attempt
Correct Answer

C. अपरिमेय संख्याIrrational number

Step 1

Concept

\(\sqrt{5}\) is not the square root of a perfect square. Therefore it is irrational.

Step 2

Why this answer is correct

The correct answer is C. अपरिमेय संख्या / Irrational number. \(\sqrt{5}\) is not the square root of a perfect square. Therefore it is irrational.

Step 3

Exam Tip

\(\sqrt{5}\) पूर्ण वर्ग का वर्गमूल नहीं है। इसलिए यह अपरिमेय संख्या है।

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वर्गमूल सर्पिल में समकोण बनाने के लिए कितने डिग्री का कोण चाहिए?

What angle is needed to make a right angle in a square root spiral?

Explanation opens after your attempt
Correct Answer

D. \(90^\circ\)

Step 1

Concept

A right angle is \(90^\circ\). Pythagoras theorem applies to this angle.

Step 2

Why this answer is correct

The correct answer is D. \(90^\circ\). A right angle is \(90^\circ\). Pythagoras theorem applies to this angle.

Step 3

Exam Tip

समकोण \(90^\circ\) का होता है। इसी पर पाइथागोरस प्रमेय लागू होता है।

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\(\sqrt{n}\) कर्ण पर (1) इकाई लंब जोड़ने पर नया कर्ण सामान्यतः क्या होगा?

If a (1) unit perpendicular is added to the hypotenuse \(\sqrt{n}\), what will the new hypotenuse generally be?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{n+1}\)

Step 1

Concept

By Pythagoras the new hypotenuse is (\sqrt{\(\sqrt{n}\)2+12}=\sqrt{n+1}). This is the general rule.

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{n+1}\). By Pythagoras the new hypotenuse is (\sqrt{\(\sqrt{n}\)2+12}=\sqrt{n+1}). This is the general rule.

Step 3

Exam Tip

पाइथागोरस से नया कर्ण (\sqrt{\(\sqrt{n}\)2+12}=\sqrt{n+1}) होता है। यही सामान्य नियम है।

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वर्गमूल सर्पिल में \(\sqrt{20}\) के बाद अगला कर्ण कौन-सा होगा?

In a square root spiral, which hypotenuse comes after \(\sqrt{20}\)?

Explanation opens after your attempt
Correct Answer

C. \(\sqrt{21}\)

Step 1

Concept

At every step the next square root appears. Therefore \(\sqrt{21}\) comes after \(\sqrt{20}\).

Step 2

Why this answer is correct

The correct answer is C. \(\sqrt{21}\). At every step the next square root appears. Therefore \(\sqrt{21}\) comes after \(\sqrt{20}\).

Step 3

Exam Tip

हर चरण में अगला वर्गमूल आता है। इसलिए \(\sqrt{20}\) के बाद \(\sqrt{21}\) होगा।

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वर्गमूल सर्पिल से मिली लंबाई को संख्या रेखा पर रखने के लिए कौन-सा उपकरण उपयोगी है?

Which tool is useful to place the length obtained from a square root spiral on the number line?

Explanation opens after your attempt
Correct Answer

A. कंपासCompass

Step 1

Concept

A compass transfers the hypotenuse length to the number line. This gives the correct point.

Step 2

Why this answer is correct

The correct answer is A. कंपास / Compass. A compass transfers the hypotenuse length to the number line. This gives the correct point.

Step 3

Exam Tip

कंपास से कर्ण की लंबाई संख्या रेखा पर स्थानांतरित की जाती है। इससे सही बिंदु मिलता है।

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वर्गमूल सर्पिल में \(\sqrt{2}\) संख्या रेखा पर किन संख्याओं के बीच होता है?

In a square root spiral, \(\sqrt{2}\) lies between which numbers on the number line?

Explanation opens after your attempt
Correct Answer

B. (1) और (2)(1) and (2)

Step 1

Concept

Because \(1^2<2<2^2\). Therefore \(1<\sqrt{2}<2\).

Step 2

Why this answer is correct

The correct answer is B. (1) और (2) / (1) and (2). Because \(1^2<2<2^2\). Therefore \(1<\sqrt{2}<2\).

Step 3

Exam Tip

क्योंकि \(1^2<2<2^2\) है। इसलिए \(1<\sqrt{2}<2\) होता है।

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\(\sqrt{10}\) संख्या रेखा पर किन पूर्ण संख्याओं के बीच होगा?

Between which whole numbers will \(\sqrt{10}\) lie on the number line?

Explanation opens after your attempt
Correct Answer

C. (3) और (4)(3) and (4)

Step 1

Concept

Because \(3^2<10<4^2\). Therefore \(3<\sqrt{10}<4\).

Step 2

Why this answer is correct

The correct answer is C. (3) और (4) / (3) and (4). Because \(3^2<10<4^2\). Therefore \(3<\sqrt{10}<4\).

Step 3

Exam Tip

क्योंकि \(3^2<10<4^2\) है। इसलिए \(3<\sqrt{10}<4\) होता है।

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वर्गमूल सर्पिल में \(\sqrt{2}+1=\sqrt{3}\) मानना क्यों गलत है?

Why is it wrong to assume \(\sqrt{2}+1=\sqrt{3}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. क्योंकि नया कर्ण वर्गों के योग से बनता हैBecause the new hypotenuse is formed by the sum of squares

Step 1

Concept

In a square root spiral the addition is of squares, not direct lengths. The correct reasoning is Pythagoras theorem.

Step 2

Why this answer is correct

The correct answer is A. क्योंकि नया कर्ण वर्गों के योग से बनता है / Because the new hypotenuse is formed by the sum of squares. In a square root spiral the addition is of squares, not direct lengths. The correct reasoning is Pythagoras theorem.

Step 3

Exam Tip

वर्गमूल सर्पिल में जोड़ सीधे लंबाइयों का नहीं, वर्गों का होता है। सही तर्क पाइथागोरस प्रमेय है।

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वर्गमूल सर्पिल में बनने वाली आकृति कैसी दिखाई देती है?

What does the figure formed in a square root spiral look like?

Explanation opens after your attempt
Correct Answer

A. सर्पिल जैसीLike a spiral

Step 1

Concept

Successive right triangles are formed while changing direction. Therefore the figure looks like a spiral.

Step 2

Why this answer is correct

The correct answer is A. सर्पिल जैसी / Like a spiral. Successive right triangles are formed while changing direction. Therefore the figure looks like a spiral.

Step 3

Exam Tip

लगातार समकोण त्रिभुज दिशा बदलते हुए बनते हैं। इसलिए आकृति सर्पिल जैसी दिखती है।

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वर्गमूल सर्पिल का मुख्य उद्देश्य क्या है?

What is the main purpose of a square root spiral?

Explanation opens after your attempt
Correct Answer

A. वर्गमूल लंबाइयों का ज्यामितीय निर्माण करनाTo geometrically construct square root lengths

Step 1

Concept

A square root spiral constructs lengths like \(\sqrt{2},\sqrt{3},\sqrt{5}\). It is useful on the number line.

Step 2

Why this answer is correct

The correct answer is A. वर्गमूल लंबाइयों का ज्यामितीय निर्माण करना / To geometrically construct square root lengths. A square root spiral constructs lengths like \(\sqrt{2},\sqrt{3},\sqrt{5}\). It is useful on the number line.

Step 3

Exam Tip

वर्गमूल सर्पिल \(\sqrt{2},\sqrt{3},\sqrt{5}\) जैसी लंबाइयाँ बनाता है। यह संख्या रेखा पर उपयोगी है।

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वर्गमूल सर्पिल में \(\sqrt{18}\) बनाने से पहले कौन-सा कर्ण बन चुका होगा?

Before constructing \(\sqrt{18}\) in a square root spiral, which hypotenuse will already be constructed?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{17}\)

Step 1

Concept

Adding a (1) unit perpendicular to \(\sqrt{17}\) gives \(\sqrt{18}\). The previous hypotenuse has one less number.

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{17}\). Adding a (1) unit perpendicular to \(\sqrt{17}\) gives \(\sqrt{18}\). The previous hypotenuse has one less number.

Step 3

Exam Tip

\(\sqrt{17}\) में (1) इकाई लंब जोड़कर \(\sqrt{18}\) मिलता है। पिछले कर्ण की संख्या एक कम होती है।

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वर्गमूल सर्पिल में \(\sqrt{30}\) के बाद कौन-सा कर्ण आएगा?

In a square root spiral, which hypotenuse comes after \(\sqrt{30}\)?

Explanation opens after your attempt
Correct Answer

C. \(\sqrt{31}\)

Step 1

Concept

In the next step the number increases by (1). Therefore \(\sqrt{31}\) comes after \(\sqrt{30}\).

Step 2

Why this answer is correct

The correct answer is C. \(\sqrt{31}\). In the next step the number increases by (1). Therefore \(\sqrt{31}\) comes after \(\sqrt{30}\).

Step 3

Exam Tip

अगले चरण में संख्या (1) बढ़ती है। इसलिए \(\sqrt{30}\) के बाद \(\sqrt{31}\) आता है।

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वर्गमूल सर्पिल में \(\sqrt{36}\) किसके बराबर होगा?

In a square root spiral, \(\sqrt{36}\) will be equal to what?

Explanation opens after your attempt
Correct Answer

B. (6)

Step 1

Concept

\(\sqrt{36}=6\). The number (36) is a perfect square.

Step 2

Why this answer is correct

The correct answer is B. (6). \(\sqrt{36}=6\). The number (36) is a perfect square.

Step 3

Exam Tip

\(\sqrt{36}=6\) होता है। (36) पूर्ण वर्ग है।

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\(\sqrt{26}\) संख्या रेखा पर किन पूर्ण संख्याओं के बीच होगा?

Between which whole numbers will \(\sqrt{26}\) lie on the number line?

Explanation opens after your attempt
Correct Answer

B. (5) और (6)(5) and (6)

Step 1

Concept

Because \(5^2<26<6^2\). Therefore \(5<\sqrt{26}<6\).

Step 2

Why this answer is correct

The correct answer is B. (5) और (6) / (5) and (6). Because \(5^2<26<6^2\). Therefore \(5<\sqrt{26}<6\).

Step 3

Exam Tip

क्योंकि \(5^2<26<6^2\) है। इसलिए \(5<\sqrt{26}<6\) होता है।

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वर्गमूल सर्पिल में (1) इकाई लंब को \(90^\circ\) पर खींचने का कारण क्या है?

Why is the (1) unit perpendicular drawn at \(90^\circ\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. समकोण त्रिभुज बनाने के लिएTo make a right triangle

Step 1

Concept

A \(90^\circ\) angle makes a right triangle. Then Pythagoras theorem gives the new hypotenuse.

Step 2

Why this answer is correct

The correct answer is A. समकोण त्रिभुज बनाने के लिए / To make a right triangle. A \(90^\circ\) angle makes a right triangle. Then Pythagoras theorem gives the new hypotenuse.

Step 3

Exam Tip

\(90^\circ\) से समकोण त्रिभुज बनता है। फिर पाइथागोरस प्रमेय से नया कर्ण मिलता है।

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वर्गमूल सर्पिल में \(\sqrt{50}\) बनाने के लिए कौन-सा पिछला कर्ण उपयोग होगा?

Which previous hypotenuse is used to construct \(\sqrt{50}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{49}\)

Step 1

Concept

Adding a (1) unit perpendicular to \(\sqrt{49}\) gives \(\sqrt{50}\). The previous number is (1) less.

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{49}\). Adding a (1) unit perpendicular to \(\sqrt{49}\) gives \(\sqrt{50}\). The previous number is (1) less.

Step 3

Exam Tip

\(\sqrt{49}\) में (1) इकाई लंब जोड़ने पर \(\sqrt{50}\) बनता है। पिछली संख्या (1) कम होती है।

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वर्गमूल सर्पिल में \(\sqrt{49}\) की लंबाई क्या होगी?

What is the length of \(\sqrt{49}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

B. (7)

Step 1

Concept

\(\sqrt{49}=7\). The number (49) is a perfect square.

Step 2

Why this answer is correct

The correct answer is B. (7). \(\sqrt{49}=7\). The number (49) is a perfect square.

Step 3

Exam Tip

\(\sqrt{49}=7\) होता है। (49) पूर्ण वर्ग है।

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\(\sqrt{40}\) संख्या रेखा पर किन पूर्ण संख्याओं के बीच होगा?

Between which whole numbers will \(\sqrt{40}\) lie on the number line?

Explanation opens after your attempt
Correct Answer

B. (6) और (7)(6) and (7)

Step 1

Concept

Because \(6^2<40<7^2\). Therefore \(6<\sqrt{40}<7\).

Step 2

Why this answer is correct

The correct answer is B. (6) और (7) / (6) and (7). Because \(6^2<40<7^2\). Therefore \(6<\sqrt{40}<7\).

Step 3

Exam Tip

क्योंकि \(6^2<40<7^2\) है। इसलिए \(6<\sqrt{40}<7\) होता है।

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वर्गमूल सर्पिल में \(\sqrt{6}\) से नया कर्ण बनाने पर कौन-सा कर्ण मिलेगा?

If a new hypotenuse is made from \(\sqrt{6}\) in a square root spiral, which hypotenuse is obtained?

Explanation opens after your attempt
Correct Answer

C. \(\sqrt{7}\)

Step 1

Concept

Adding a (1) unit perpendicular to \(\sqrt{6}\) forms \(\sqrt{7}\). This follows from Pythagoras theorem.

Step 2

Why this answer is correct

The correct answer is C. \(\sqrt{7}\). Adding a (1) unit perpendicular to \(\sqrt{6}\) forms \(\sqrt{7}\). This follows from Pythagoras theorem.

Step 3

Exam Tip

\(\sqrt{6}\) में (1) इकाई लंब जोड़ने से \(\sqrt{7}\) बनता है। यह पाइथागोरस प्रमेय से आता है।

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वर्गमूल सर्पिल में \(\sqrt{64}\) किस संख्या के बराबर है?

In a square root spiral, \(\sqrt{64}\) is equal to which number?

Explanation opens after your attempt
Correct Answer

C. (8)

Step 1

Concept

\(\sqrt{64}=8\). Recognizing perfect squares gives the answer quickly.

Step 2

Why this answer is correct

The correct answer is C. (8). \(\sqrt{64}=8\). Recognizing perfect squares gives the answer quickly.

Step 3

Exam Tip

\(\sqrt{64}=8\) होता है। पूर्ण वर्गों की पहचान से उत्तर जल्दी मिलता है।

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वर्गमूल सर्पिल में \(\sqrt{2}\) किस प्रकार की संख्या है?

In a square root spiral, what type of number is \(\sqrt{2}\)?

Explanation opens after your attempt
Correct Answer

A. अपरिमेय संख्याIrrational number

Step 1

Concept

\(\sqrt{2}\) is not the square root of a perfect square. Therefore it is irrational.

Step 2

Why this answer is correct

The correct answer is A. अपरिमेय संख्या / Irrational number. \(\sqrt{2}\) is not the square root of a perfect square. Therefore it is irrational.

Step 3

Exam Tip

\(\sqrt{2}\) किसी पूर्ण वर्ग का वर्गमूल नहीं है। इसलिए यह अपरिमेय संख्या है।

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वर्गमूल सर्पिल में \(\sqrt{15}\) बनाने से ठीक पहले कौन-सा कर्ण होगा?

Just before constructing \(\sqrt{15}\) in a square root spiral, which hypotenuse will be present?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{14}\)

Step 1

Concept

With \(\sqrt{14}\) and a (1) unit perpendicular, \(\sqrt{15}\) is formed. The previous hypotenuse has one less number.

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{14}\). With \(\sqrt{14}\) and a (1) unit perpendicular, \(\sqrt{15}\) is formed. The previous hypotenuse has one less number.

Step 3

Exam Tip

\(\sqrt{14}\) के साथ (1) इकाई लंब से \(\sqrt{15}\) बनता है। पिछला कर्ण एक कम संख्या का है।

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वर्गमूल सर्पिल में \(\sqrt{24}\) के बाद कौन-सा कर्ण बनेगा?

In a square root spiral, which hypotenuse will be formed after \(\sqrt{24}\)?

Explanation opens after your attempt
Correct Answer

C. \(\sqrt{25}\)

Step 1

Concept

In the next step \(\sqrt{24+1}=\sqrt{25}\) is formed. The number increases by (1).

Step 2

Why this answer is correct

The correct answer is C. \(\sqrt{25}\). In the next step \(\sqrt{24+1}=\sqrt{25}\) is formed. The number increases by (1).

Step 3

Exam Tip

अगले चरण में \(\sqrt{24+1}=\sqrt{25}\) बनता है। संख्या क्रम में (1) बढ़ती है।

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वर्गमूल सर्पिल से \(\sqrt{3}\) को संख्या रेखा पर अंकित करने के लिए किस लंबाई को कंपास में लेना होगा?

To mark \(\sqrt{3}\) on the number line from a square root spiral, which length should be taken in the compass?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{3}\) का कर्णHypotenuse of \(\sqrt{3}\)

Step 1

Concept

The hypotenuse length of the required square root is taken in the compass. So the hypotenuse of \(\sqrt{3}\) is needed.

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{3}\) का कर्ण / Hypotenuse of \(\sqrt{3}\). The hypotenuse length of the required square root is taken in the compass. So the hypotenuse of \(\sqrt{3}\) is needed.

Step 3

Exam Tip

जिस वर्गमूल को अंकित करना है, उसी कर्ण की लंबाई कंपास में लेते हैं। इसलिए \(\sqrt{3}\) का कर्ण चाहिए।

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वर्गमूल सर्पिल में \(\sqrt{3}\) किन पूर्ण संख्याओं के बीच स्थित है?

In a square root spiral, \(\sqrt{3}\) lies between which whole numbers?

Explanation opens after your attempt
Correct Answer

B. (1) और (2)(1) and (2)

Step 1

Concept

Because \(1^2<3<2^2\). Therefore \(\sqrt{3}\) lies between (1) and (2).

Step 2

Why this answer is correct

The correct answer is B. (1) और (2) / (1) and (2). Because \(1^2<3<2^2\). Therefore \(\sqrt{3}\) lies between (1) and (2).

Step 3

Exam Tip

क्योंकि \(1^2<3<2^2\) है। इसलिए \(\sqrt{3}\) (1) और (2) के बीच है।

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वर्गमूल सर्पिल में सेट स्क्वायर का उपयोग किसलिए किया जा सकता है?

For what can a set square be used in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. \(90^\circ\) का कोण बनाने के लिएTo make a \(90^\circ\) angle

Step 1

Concept

A set square helps make a right angle easily. A correct right angle gives the correct hypotenuse.

Step 2

Why this answer is correct

The correct answer is A. \(90^\circ\) का कोण बनाने के लिए / To make a \(90^\circ\) angle. A set square helps make a right angle easily. A correct right angle gives the correct hypotenuse.

Step 3

Exam Tip

सेट स्क्वायर से समकोण आसानी से बनता है। सही समकोण से सही कर्ण मिलता है।

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वर्गमूल सर्पिल में \(\sqrt{72}\) किस दो पूर्ण संख्याओं के बीच होगा?

In a square root spiral, \(\sqrt{72}\) lies between which two whole numbers?

Explanation opens after your attempt
Correct Answer

C. (8) और (9)(8) and (9)

Step 1

Concept

Because \(8^2<72<9^2\). Therefore \(8<\sqrt{72}<9\).

Step 2

Why this answer is correct

The correct answer is C. (8) और (9) / (8) and (9). Because \(8^2<72<9^2\). Therefore \(8<\sqrt{72}<9\).

Step 3

Exam Tip

क्योंकि \(8^2<72<9^2\) है। इसलिए \(8<\sqrt{72}<9\) होता है।

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वर्गमूल सर्पिल में \(\sqrt{80}\) बनाने के लिए पिछला कर्ण कौन-सा होगा?

To construct \(\sqrt{80}\) in a square root spiral, which previous hypotenuse will be used?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{79}\)

Step 1

Concept

Adding a (1) unit perpendicular to \(\sqrt{79}\) gives \(\sqrt{80}\). The previous hypotenuse has one less number.

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{79}\). Adding a (1) unit perpendicular to \(\sqrt{79}\) gives \(\sqrt{80}\). The previous hypotenuse has one less number.

Step 3

Exam Tip

\(\sqrt{79}\) पर (1) इकाई लंब जोड़ने से \(\sqrt{80}\) बनता है। पिछला कर्ण एक कम संख्या का होता है।

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वर्गमूल सर्पिल में \(\sqrt{81}\) की लंबाई क्या होगी?

What is the length of \(\sqrt{81}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

C. (9)

Step 1

Concept

\(\sqrt{81}=9\). The number (81) is a perfect square.

Step 2

Why this answer is correct

The correct answer is C. (9). \(\sqrt{81}=9\). The number (81) is a perfect square.

Step 3

Exam Tip

\(\sqrt{81}=9\) होता है। (81) पूर्ण वर्ग है।

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वर्गमूल सर्पिल में \(\sqrt{2}\) बनाने के बाद कौन-सा निर्माण करना होता है?

After constructing \(\sqrt{2}\) in a square root spiral, what construction is done next?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{2}\) के सिरे पर (1) इकाई लंब बनानाDraw a (1) unit perpendicular at the end of \(\sqrt{2}\)

Step 1

Concept

A (1) unit perpendicular is drawn at the end of \(\sqrt{2}\) to make the next triangle. This gives \(\sqrt{3}\).

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{2}\) के सिरे पर (1) इकाई लंब बनाना / Draw a (1) unit perpendicular at the end of \(\sqrt{2}\). A (1) unit perpendicular is drawn at the end of \(\sqrt{2}\) to make the next triangle. This gives \(\sqrt{3}\).

Step 3

Exam Tip

\(\sqrt{2}\) के सिरे पर (1) इकाई लंब बनाकर अगला त्रिभुज बनाया जाता है। इससे \(\sqrt{3}\) मिलता है।

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वर्गमूल सर्पिल में \(\sqrt{4}\) के बाद बनने वाला \(\sqrt{5}\) किस प्रकार की संख्या है?

In a square root spiral, what type of number is \(\sqrt{5}\) formed after \(\sqrt{4}\)?

Explanation opens after your attempt
Correct Answer

A. अपरिमेय संख्याIrrational number

Step 1

Concept

\(\sqrt{5}\) is not the square root of a perfect square. Therefore it is irrational.

Step 2

Why this answer is correct

The correct answer is A. अपरिमेय संख्या / Irrational number. \(\sqrt{5}\) is not the square root of a perfect square. Therefore it is irrational.

Step 3

Exam Tip

\(\sqrt{5}\) पूर्ण वर्ग का वर्गमूल नहीं है। इसलिए यह अपरिमेय है।

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वर्गमूल सर्पिल में \(\sqrt{100}\) किस संख्या के बराबर होगा?

In a square root spiral, \(\sqrt{100}\) will be equal to which number?

Explanation opens after your attempt
Correct Answer

B. (10)

Step 1

Concept

\(\sqrt{100}=10\). Square roots of perfect squares give whole numbers.

Step 2

Why this answer is correct

The correct answer is B. (10). \(\sqrt{100}=10\). Square roots of perfect squares give whole numbers.

Step 3

Exam Tip

\(\sqrt{100}=10\) होता है। पूर्ण वर्गों के वर्गमूल पूर्ण संख्या देते हैं।

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वर्गमूल सर्पिल में \(\sqrt{101}\) किस दो पूर्ण संख्याओं के बीच होगा?

In a square root spiral, \(\sqrt{101}\) lies between which two whole numbers?

Explanation opens after your attempt
Correct Answer

B. (10) और (11)(10) and (11)

Step 1

Concept

Because \(10^2<101<11^2\). Therefore \(10<\sqrt{101}<11\).

Step 2

Why this answer is correct

The correct answer is B. (10) और (11) / (10) and (11). Because \(10^2<101<11^2\). Therefore \(10<\sqrt{101}<11\).

Step 3

Exam Tip

क्योंकि \(10^2<101<11^2\) है। इसलिए \(10<\sqrt{101}<11\) होता है।

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वर्गमूल सर्पिल में कौन-सा कथन \(\sqrt{n}\) से \(\sqrt{n+1}\) बनने को सही समझाता है?

Which statement correctly explains how \(\sqrt{n}\) becomes \(\sqrt{n+1}\) in a square root spiral?

Explanation opens after your attempt
Correct Answer

A. पिछले कर्ण और (1) इकाई लंब के वर्गों का योग लिया जाता हैThe sum of squares of previous hypotenuse and (1) unit perpendicular is taken

Step 1

Concept

Pythagoras theorem uses the sum of squares. Therefore the new hypotenuse becomes \(\sqrt{n+1}\).

Step 2

Why this answer is correct

The correct answer is A. पिछले कर्ण और (1) इकाई लंब के वर्गों का योग लिया जाता है / The sum of squares of previous hypotenuse and (1) unit perpendicular is taken. Pythagoras theorem uses the sum of squares. Therefore the new hypotenuse becomes \(\sqrt{n+1}\).

Step 3

Exam Tip

पाइथागोरस प्रमेय में वर्गों का योग आता है। इसलिए नया कर्ण \(\sqrt{n+1}\) बनता है।

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वर्गमूल सर्पिल में \(\sqrt{2}\) की लंबाई संख्या रेखा पर अंकित करते समय चाप कहाँ से खींचा जाता है?

While marking \(\sqrt{2}\) on the number line from a square root spiral, from where is the arc drawn?

Explanation opens after your attempt
Correct Answer

A. मूल बिंदु सेFrom the origin

Step 1

Concept

The compass point is kept at the origin and an arc is drawn. This locates \(\sqrt{2}\).

Step 2

Why this answer is correct

The correct answer is A. मूल बिंदु से / From the origin. The compass point is kept at the origin and an arc is drawn. This locates \(\sqrt{2}\).

Step 3

Exam Tip

कंपास की नोक मूल बिंदु पर रखकर चाप खींचते हैं। इससे \(\sqrt{2}\) का स्थान मिलता है।

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वर्गमूल सर्पिल का मुख्य विचार एक पंक्ति में कौन-सा है?

What is the main idea of a square root spiral in one line?

Explanation opens after your attempt
Correct Answer

A. समकोण त्रिभुजों से क्रमिक वर्गमूल लंबाइयाँ बनानाMaking successive square root lengths using right triangles

Step 1

Concept

Each new right triangle gives the next square root. This is the basic idea of a square root spiral.

Step 2

Why this answer is correct

The correct answer is A. समकोण त्रिभुजों से क्रमिक वर्गमूल लंबाइयाँ बनाना / Making successive square root lengths using right triangles. Each new right triangle gives the next square root. This is the basic idea of a square root spiral.

Step 3

Exam Tip

हर नया समकोण त्रिभुज अगला वर्गमूल देता है। यही वर्गमूल सर्पिल का मूल विचार है।

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वर्गमूल सर्पिल में \(\sqrt{121}\) की लंबाई किस संख्या के बराबर होगी?

In a square root spiral, the length \(\sqrt{121}\) will be equal to which number?

Explanation opens after your attempt
Correct Answer

B. (11)

Step 1

Concept

\(\sqrt{121}=11\). Since (121) is a perfect square, its square root is a whole number.

Step 2

Why this answer is correct

The correct answer is B. (11). \(\sqrt{121}=11\). Since (121) is a perfect square, its square root is a whole number.

Step 3

Exam Tip

\(\sqrt{121}=11\) होता है। (121) पूर्ण वर्ग है, इसलिए उसका वर्गमूल पूर्ण संख्या है।

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वर्गमूल सर्पिल में \(\sqrt{57}\) बनाने के लिए किस पिछले कर्ण पर (1) इकाई लंब बनाई जाएगी?

To construct \(\sqrt{57}\) in a square root spiral, a (1) unit perpendicular will be drawn on which previous hypotenuse?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{56}\)

Step 1

Concept

Adding a (1) unit perpendicular to \(\sqrt{56}\) forms \(\sqrt{57}\). The previous hypotenuse number is always (1) less.

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{56}\). Adding a (1) unit perpendicular to \(\sqrt{56}\) forms \(\sqrt{57}\). The previous hypotenuse number is always (1) less.

Step 3

Exam Tip

\(\sqrt{56}\) के साथ (1) इकाई लंब जोड़ने पर \(\sqrt{57}\) बनता है। पिछले कर्ण की संख्या हमेशा (1) कम होती है।

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वर्गमूल सर्पिल में \(\sqrt{43}\) के बाद अगला कर्ण कौन-सा बनेगा?

In a square root spiral, which hypotenuse will be formed after \(\sqrt{43}\)?

Explanation opens after your attempt
Correct Answer

C. \(\sqrt{44}\)

Step 1

Concept

At each new step, a (1) unit perpendicular is added. Therefore \(\sqrt{44}\) will be formed after \(\sqrt{43}\).

Step 2

Why this answer is correct

The correct answer is C. \(\sqrt{44}\). At each new step, a (1) unit perpendicular is added. Therefore \(\sqrt{44}\) will be formed after \(\sqrt{43}\).

Step 3

Exam Tip

हर नए चरण में (1) इकाई लंब जुड़ती है। इसलिए \(\sqrt{43}\) के बाद \(\sqrt{44}\) बनेगा।

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वर्गमूल सर्पिल बनाते समय (1) इकाई की दूरी सही मापने के लिए कौन-सा उपकरण उपयोगी है?

Which tool is useful for measuring the (1) unit distance correctly while making a square root spiral?

Explanation opens after your attempt
Correct Answer

A. मापक पट्टीRuler

Step 1

Concept

A ruler is useful for taking the (1) unit length correctly. Wrong measurement can make the spiral lengths incorrect.

Step 2

Why this answer is correct

The correct answer is A. मापक पट्टी / Ruler. A ruler is useful for taking the (1) unit length correctly. Wrong measurement can make the spiral lengths incorrect.

Step 3

Exam Tip

(1) इकाई की लंबाई सही लेने के लिए मापक पट्टी उपयोगी है। गलत माप से सर्पिल की लंबाइयाँ गलत हो सकती हैं।

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FAQs

Class 9 Mathematics Quiz FAQs

How many questions are in this quiz?

This level is designed for 50 active questions. Currently 50 questions are available for the selected class and difficulty.

Is there a timer in this quiz?

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Can I open each question separately?

Yes, every question has its own SEO-friendly page with answer, explanation and related practice links.