Muft Shiksha
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

Subjects
Class 9MathematicsNumber SystemsProof of irrationality of square root 2 and square root 3MediumLevel 17
0 reads0 ratings0 helpful

In the proof of (\sqrt{3}), (p^2=3q^2) gives (p=3k) and then (q^2=3k^2). What will be the final conclusion?

Advertisement

Answer and explanation

Correct answer: (\sqrt{3}) is irrational

From (q^2=3k^2), (q) is also divisible by (3). Both (p) and (q) divisible by (3) contradicts the coprime condition.

Related tags

Number-SystemsSqrt3Final-Conclusion

Frequently asked questions

What is the correct answer to this question?

(\sqrt{3}) is irrational

Why is this the correct answer?

From (q^2=3k^2), (q) is also divisible by (3). Both (p) and (q) divisible by (3) contradicts the coprime condition.

Which subject and chapter does this question cover?

This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Proof of irrationality of square root 2 and square root 3.

Was this question useful?

No ratings yetWrite a review / Rate this question

Student Reviews

No published reviews yet.

KEEP PRACTISING

10 more MCQs
  1. 1If \(x=3-\sqrt5\), what is \(\frac1x\)?
  2. 2What assumption is taken first to prove the irrationality of (\sqrt{2})?
  3. 3If (\sqrt{2}=\frac{p}{q}) is assumed then which condition is necessary for (p) and (q)?
  4. 4Which of the following numbers is irrational and can be proved irrational using a contradiction based on divisibility by 3?
  5. 5From (p^2=2q^2) what conclusion is obtained about (p^2)?
  6. 6If (p^2) is even then what is the correct conclusion about (p)?
  7. 7A student sees \(\sqrt{3}\) displayed as 1.732 on a calculator and claims that \(\sqrt{3}\) is rational because the decimal ends. Which statement correctly identifies the error?
  8. 8If (p=2r) and (p^2=2q^2), which conclusion follows next?
  9. 9From (q^2=2r^2) what conclusion follows about (q)?
  10. 10What is the final contradiction in the proof that √2 is irrational?
Advertisement