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 10MathematicsReal NumbersProof of irrationality of √2, √3, √5HardLevel 18
0 reads0 ratings0 helpful

In the proof that (\sqrt{2}) is irrational, what conclusion is obtained after putting (p=2k)?

Advertisement

Answer and explanation

Correct answer: (q^2=2k^2), so (q) is even

Step 1: From (p^2=2q^2) and (p=2k), we get (4k^2=2q^2). Step 2: Simplifying gives (q^2=2k^2), so (q^2) and (q) are even. Step 3: This second evenness completes the contradiction.

Related tags

Real-NumbersRoot2ContradictionEven-NumbersHard

Frequently asked questions

What is the correct answer to this question?

(q^2=2k^2), so (q) is even

Why is this the correct answer?

Step 1: From (p^2=2q^2) and (p=2k), we get (4k^2=2q^2). Step 2: Simplifying gives (q^2=2k^2), so (q^2) and (q) are even. Step 3: This second evenness completes the contradiction.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Proof of irrationality of √2, √3, √5.

Was this question useful?

No ratings yetWrite a review / Rate this question

Student Reviews

No published reviews yet.

KEEP PRACTISING

10 more MCQs
  1. 1Which assumption is taken first to prove that (\sqrt{2}) is irrational?
  2. 2If (\sqrt{2}=\frac{p}{q}), what is obtained after squaring both sides?
  3. 3From the equation (p^2=2q^2), what do we learn about (p^2)?
  4. 4If (p^2) is even, which conclusion about (p) is correct?
  5. 5If (p) is even, in which form can (p) be written?
  6. 6What conclusion is obtained by putting (p=2k) in (p^2=2q^2)?
  7. 7What is the final contradiction in the proof of (\sqrt{2})?
  8. 8What is the correct final conclusion of the proof of (\sqrt{2})?
  9. 9If (\sqrt{3}) is assumed rational, in which form is it written?
  10. 10If (\sqrt{3}=\frac{p}{q}), which equation is obtained after squaring?
Advertisement