Question

proof of √3 is irrational
4th step answer it ( class 10th )​

Answer 1

Answer:

Let us assume that√3 is rational

√3 = p/q, q not equal to 0

squaring on both sides

(√3)^2 = (p/q)^2

3 = p^2/q^2

by cross multiplication

3q^2 = p^2...........1

p^2 is multiple of 3

p is multiple of 3

3q^2 = (3k)^2

3q^2 = 3^2k^2

q^2 = 3k^2......2

q^2 is multiple of 3

q is multiple of 3

therefore (p,q) = 3

our assume is wrong

so, √3 is irrational.