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 3ExpertLevel 17
0 reads0 ratings0 helpful

Why is only (r^2) being even not the final contradiction in the proof of (\sqrt{2})?

Advertisement

Answer and explanation

Correct answer: Because first (r) and then (s) must both be proved even

The contradiction with lowest fraction forms only when numerator and denominator both have common factor (2). Only (r^2) being even is a middle step.

Related tags

Number-SystemsSqrt2Proof-GapExpert

Frequently asked questions

What is the correct answer to this question?

Because first (r) and then (s) must both be proved even

Why is this the correct answer?

The contradiction with lowest fraction forms only when numerator and denominator both have common factor (2). Only (r^2) being even is a middle step.

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. 1What assumption is taken first to prove the irrationality of (\sqrt{2})?
  2. 2If (\sqrt{2}=\frac{p}{q}) is assumed then which condition is necessary for (p) and (q)?
  3. 3Which of the following numbers is irrational and can be proved irrational using a contradiction based on divisibility by 3?
  4. 4From (p^2=2q^2) what conclusion is obtained about (p^2)?
  5. 5If (p^2) is even then what is the correct conclusion about (p)?
  6. 6A 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?
  7. 7If (p=2r) and (p^2=2q^2), which conclusion follows next?
  8. 8From (q^2=2r^2) what conclusion follows about (q)?
  9. 9What is the final contradiction in the proof that √2 is irrational?
  10. 10Which method is used in the proof of the irrationality of √2?
Advertisement