Question

Assuming that √7 is a rational number prove that 4-3√7 is an irrational number

Answer 1

Let us assume that 4-3√7 is rational number

4-3√7=a/b. {where a and b are the integers}

-3√7=a-4b/b

=>√7=a-4b/-3b

As a/b is rational

so a-4b/-3b is also rational

Here we assumed that √7 is rational number.

But this contradicts the fact that √7 is irrational so our assumption is wrong

Therefore, 4-3√7 is irrational number.