Question

Prove that 7+3root3 is not a rational no.​

Answer 1

$\huge\underline\mathtt{Solution:-}$

Let us suppose that

$7 + 3 \sqrt{3}$

is rational

$7 + 3 \sqrt{3} = \frac{x}{y} \\ 3 \sqrt{3} = \frac{x}{y} - 7 \\ 3 \sqrt{3} = \frac{x - 7y}{y} \\ \sqrt{3} = \frac{x - 7y}{3y}$

This means that √3 is rational which contradicts the facts that √3 is irrational.

So,our supposition is wrong

=>7+3√3 is irrational.