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 65
0 reads0 ratings0 helpful

What is the correct difference between the roles of (q\neq0) and (\gcd(p,q)=1) in the proof of (\sqrt{3})?

Advertisement

Answer and explanation

Correct answer: (q\neq0) keeps the fraction defined and (\gcd(p,q)=1) gives final contradiction

(q\neq0) is necessary for a rational fraction. (\gcd(p,q)=1) breaks when both are divisible by (3).

Related tags

Number-SystemsDenominator-GcdSqrt3

Frequently asked questions

What is the correct answer to this question?

(q\neq0) keeps the fraction defined and (\gcd(p,q)=1) gives final contradiction

Why is this the correct answer?

(q\neq0) is necessary for a rational fraction. (\gcd(p,q)=1) breaks when both are divisible by (3).

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