Update
Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है • Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है • Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है
Subjects List
Topic Wise MCQ

Mathematics Proof of irrationality of square root 2 and square root 3 MCQ Questions for Class 9

Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.

Back to Chapter Subject Page
Share

Start Proof of irrationality of square root 2 and square root 3 Topic Quiz

Difficulty select karke sirf is topic ke focused MCQs practice karein. Score, timer aur explanations student-friendly flow me milenge.

Easy Test 150 Questions Medium Test 150 Questions Hard Test 150 Questions Expert Test 199 Questions
Topic Navigation

Continue Chapter Revision

Previous Topic Next Topic Leaderboard
Chapter Revision

Related Topics

Same chapter ke nearby topics ko revise jarur karein. Exam preparation ke liye yeh topics important hain. jisme niche ke ye 8 Topics hain.

8 topics
01 Practice Topic Rational numbers 51 MCQs 02 Practice Topic Real Numbers 600 MCQs 03 Practice Topic Exponents 600 MCQs 04 Practice Topic Number line 600 MCQs 05 Practice Topic Decimal representation 600 MCQs 06 Practice Topic Irrational numbers 600 MCQs 07 Practice Topic Square root spiral 650 MCQs 08 Practice Topic General chapter practice 50 MCQs

Proof of irrationality of square root 2 and square root 3 Practice Questions

Showing 1-10 of 649 questions.

Search
Question 1/649 Easy Mathematics Number Systems Proof of irrationality of square root 2 and square root 3 Class 9 Level 19

\(\sqrt{2}\) की अपरिमेयता सिद्ध करने में सबसे पहले कौन-सी मान्यता ली जाती है?

What assumption is taken first to prove the irrationality of \(\sqrt{2}\)?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{2}\) परिमेय है\(\sqrt{2}\) is rational

Step 1

Concept

In contradiction method we first assume \(\sqrt{2}\) is rational. Then a contradiction is obtained from this assumption.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{2}\) परिमेय है / \(\sqrt{2}\) is rational. In contradiction method we first assume \(\sqrt{2}\) is rational. Then a contradiction is obtained from this assumption.

Step 3

Exam Tip

विरोधाभास विधि में पहले \(\sqrt{2}\) को परिमेय मानते हैं। फिर इसी मान्यता से विरोधाभास निकाला जाता है।

Open Question Page
Ask Friends
Question 2/649 Easy Mathematics Number Systems Proof of irrationality of square root 2 and square root 3 Class 9 Level 19

यदि \(\sqrt{2}=\frac{p}{q}\) माना जाए तो (p) और (q) के लिए कौन-सी शर्त जरूरी है?

If \(\sqrt{2}=\frac{p}{q}\) is assumed then which condition is necessary for (p) and (q)?

Explanation opens after your attempt
Correct Answer

B. वे सहभाज्य होंThey are coprime

Step 1

Concept

A rational number is written in lowest form as \(\frac{p}{q}\). So (p) and (q) are assumed coprime.

Step 2

Why this answer is correct

The correct answer is B. वे सहभाज्य हों / They are coprime. A rational number is written in lowest form as \(\frac{p}{q}\). So (p) and (q) are assumed coprime.

Step 3

Exam Tip

परिमेय संख्या को न्यूनतम रूप में \(\frac{p}{q}\) लिखा जाता है। इसलिए (p) और (q) सहभाज्य माने जाते हैं।

Open Question Page
Ask Friends
Question 3/649 Easy Mathematics Number Systems Proof of irrationality of square root 2 and square root 3 Class 9 Level 19

\(\sqrt{2}=\frac{p}{q}\) को वर्ग करने पर कौन-सा संबंध मिलता है?

Which relation is obtained by squaring \(\sqrt{2}=\frac{p}{q}\)?

Explanation opens after your attempt
Correct Answer

C. \(p^2=2q^2\)

Step 1

Concept

Squaring gives \(2=\frac{p^2}{q^2}\). Hence \(p^2=2q^2\).

Step 2

Why this answer is correct

The correct answer is C. \(p^2=2q^2\). Squaring gives \(2=\frac{p^2}{q^2}\). Hence \(p^2=2q^2\).

Step 3

Exam Tip

वर्ग करने पर \(2=\frac{p^2}{q^2}\) मिलता है। इससे \(p^2=2q^2\) बनता है।

Open Question Page
Ask Friends
Question 4/649 Easy Mathematics Number Systems Proof of irrationality of square root 2 and square root 3 Class 9 Level 19

संबंध \(p^2=2q^2\) से \(p^2\) के बारे में क्या निष्कर्ष मिलता है?

From \(p^2=2q^2\) what conclusion is obtained about \(p^2\)?

Explanation opens after your attempt
Correct Answer

D. \(p^2\) सम है\(p^2\) is even

Step 1

Concept

Since \(p^2\) has factor (2), \(p^2\) is even. Recognising evenness is a key step in this proof.

Step 2

Why this answer is correct

The correct answer is D. \(p^2\) सम है / \(p^2\) is even. Since \(p^2\) has factor (2), \(p^2\) is even. Recognising evenness is a key step in this proof.

Step 3

Exam Tip

क्योंकि \(p^2\) में (2) का गुणनखंड है इसलिए \(p^2\) सम है। समता पहचानना इस प्रमाण का मुख्य चरण है।

Open Question Page
Ask Friends
Question 5/649 Easy Mathematics Number Systems Proof of irrationality of square root 2 and square root 3 Class 9 Level 19

यदि \(p^2\) सम है तो (p) के बारे में सही निष्कर्ष क्या है?

If \(p^2\) is even then what is the correct conclusion about (p)?

Explanation opens after your attempt
Correct Answer

A. (p) सम है(p) is even

Step 1

Concept

If the square of a number is even then the number is also even. This fact is used in the proof for \(\sqrt{2}\).

Step 2

Why this answer is correct

The correct answer is A. (p) सम है / (p) is even. If the square of a number is even then the number is also even. This fact is used in the proof for \(\sqrt{2}\).

Step 3

Exam Tip

यदि किसी संख्या का वर्ग सम है तो वह संख्या भी सम होती है। यही तथ्य \(\sqrt{2}\) के प्रमाण में उपयोग होता है।

Open Question Page
Ask Friends
Question 6/649 Easy Mathematics Number Systems Proof of irrationality of square root 2 and square root 3 Class 9 Level 19

\(\sqrt{2}\) के प्रमाण में (p) सम होने पर (p) को किस रूप में लिखा जाता है?

In the proof of \(\sqrt{2}\), if (p) is even then how is (p) written?

Explanation opens after your attempt
Correct Answer

A. (p=2r)

Step 1

Concept

An even number is written as a multiple of (2). So (p=2r) is taken.

Step 2

Why this answer is correct

The correct answer is A. (p=2r). An even number is written as a multiple of (2). So (p=2r) is taken.

Step 3

Exam Tip

सम संख्या को (2) के गुणज के रूप में लिखा जाता है। इसलिए (p=2r) रखा जाता है।

Open Question Page
Ask Friends
Question 7/649 Easy Mathematics Number Systems Proof of irrationality of square root 2 and square root 3 Class 9 Level 19

यदि (p=2r) और \(p^2=2q^2\) है तो आगे कौन-सा निष्कर्ष मिलता है?

If (p=2r) and \(p^2=2q^2\), which conclusion follows next?

Explanation opens after your attempt
Correct Answer

B. \(q^2=2r^2\)

Step 1

Concept

Putting (p=2r) gives \(4r^2=2q^2\). Hence \(q^2=2r^2\).

Step 2

Why this answer is correct

The correct answer is B. \(q^2=2r^2\). Putting (p=2r) gives \(4r^2=2q^2\). Hence \(q^2=2r^2\).

Step 3

Exam Tip

(p=2r) रखने पर \(4r^2=2q^2\) मिलता है। इससे \(q^2=2r^2\) बनता है।

Open Question Page
Ask Friends
Question 8/649 Easy Mathematics Number Systems Proof of irrationality of square root 2 and square root 3 Class 9 Level 19

\(q^2=2r^2\) से (q) के बारे में क्या निष्कर्ष निकलता है?

From \(q^2=2r^2\) what conclusion follows about (q)?

Explanation opens after your attempt
Correct Answer

C. (q) सम है(q) is even

Step 1

Concept

Since \(q^2\) is even, (q) is also even. This makes both (p) and (q) even.

Step 2

Why this answer is correct

The correct answer is C. (q) सम है / (q) is even. Since \(q^2\) is even, (q) is also even. This makes both (p) and (q) even.

Step 3

Exam Tip

\(q^2\) सम है इसलिए (q) भी सम होगा। यह (p) और (q) दोनों को सम बना देता है।

Open Question Page
Ask Friends
Question 9/649 Easy Mathematics Number Systems Proof of irrationality of square root 2 and square root 3 Class 9 Level 19

\(\sqrt{2}\) के प्रमाण में अंतिम विरोधाभास क्या होता है?

What is the final contradiction in the proof of \(\sqrt{2}\)?

Explanation opens after your attempt
Correct Answer

A. (p) और (q) दोनों सम निकलते हैंBoth (p) and (q) become even

Step 1

Concept

At the start (p) and (q) were assumed coprime. Both becoming even contradicts that assumption.

Step 2

Why this answer is correct

The correct answer is A. (p) और (q) दोनों सम निकलते हैं / Both (p) and (q) become even. At the start (p) and (q) were assumed coprime. Both becoming even contradicts that assumption.

Step 3

Exam Tip

शुरू में (p) और (q) सहभाज्य माने गए थे। दोनों का सम निकलना इसी मान्यता से विरोधाभास है।

Open Question Page
Ask Friends
Question 10/649 Easy Mathematics Number Systems Proof of irrationality of square root 2 and square root 3 Class 9 Level 19

\(\sqrt{2}\) की अपरिमेयता के प्रमाण में कौन-सी विधि उपयोग होती है?

Which method is used in the proof of irrationality of \(\sqrt{2}\)?

Explanation opens after your attempt
Correct Answer

B. विरोधाभास विधिContradiction method

Step 1

Concept

In this proof the opposite is assumed first and a contradiction is shown at the end. So it is contradiction method.

Step 2

Why this answer is correct

The correct answer is B. विरोधाभास विधि / Contradiction method. In this proof the opposite is assumed first and a contradiction is shown at the end. So it is contradiction method.

Step 3

Exam Tip

इस प्रमाण में पहले उल्टा मानकर अंत में विरोधाभास दिखाते हैं। इसलिए यह विरोधाभास विधि है।

Open Question Page
Ask Friends

Proof of irrationality of square root 2 and square root 3 Learning Links

Number Systems Chapter

All chapter topics and quizzes

Easy Proof of irrationality of square root 2 and square root 3 Test

Topic-wise timed quiz

Mathematics Subject

All chapters and levels

Search Proof of irrationality of square root 2 and square root 3

Find related MCQs
FAQs

Proof of irrationality of square root 2 and square root 3 FAQs

How can I practice Proof of irrationality of square root 2 and square root 3 MCQs?

Select Easy, Medium, Hard or Expert topic quiz on this page and answer topic-wise questions with explanations.

Are answers available for Proof of irrationality of square root 2 and square root 3 questions?

Yes, questions include answer feedback and explanations for revision.

Is this topic useful for Class 9 exams?

Yes, this topic page is arranged for chapter-wise revision and exam practice.