In the proof for (\sqrt{2}), (p^2=2q^2) shows (p^2) is even. If (p) is assumed odd, what problem occurs?

Question

Answer and explanation

Correct answer: The square of an odd number should be odd

Step 1: The square of an odd integer is always odd. Step 2: Here (p^2) is even, so (p) cannot be odd. Step 3: Thus (p) is proved even.

What is the correct answer to this question?

The square of an odd number should be odd

Why is this the correct answer?

Step 1: The square of an odd integer is always odd. Step 2: Here (p^2) is even, so (p) cannot be odd. Step 3: Thus (p) is proved even.

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.