In the proof of (\sqrt{5}), after putting (p=5k), what form of (q^2) follows from (p^2=5q^2)?

Question

Answer and explanation

Correct answer: (q^2=5k^2)

Step 1: If (p=5k), then (p^2=25k^2). Step 2: From (25k^2=5q^2), we get (q^2=5k^2). Step 3: This leads to the conclusion that (q) is divisible by (5).

What is the correct answer to this question?

(q^2=5k^2)

Why is this the correct answer?

Step 1: If (p=5k), then (p^2=25k^2). Step 2: From (25k^2=5q^2), we get (q^2=5k^2). Step 3: This leads to the conclusion that (q) is divisible by (5).

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.