If (\sqrt{2}=\frac{p}{q}) is assumed in lowest form and (p^2=2q^2) is obtained, what is the most precise reason that (p) is even?

Question

Answer and explanation

Correct answer: (p^2) is divisible by (2) and (2) is prime

Step 1: From (p^2=2q^2), we get (2\mid p^2). Step 2: Since (2) is prime, (2\mid p). Step 3: In such proofs, state the prime-factor rule clearly.

What is the correct answer to this question?

(p^2) is divisible by (2) and (2) is prime

Why is this the correct answer?

Step 1: From (p^2=2q^2), we get (2\mid p^2). Step 2: Since (2) is prime, (2\mid p). Step 3: In such proofs, state the prime-factor rule clearly.

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.