Question

prove that 3root2 is an irrational

Answer 1

Step-by-step explanation:

Let us assume that 3√2 is a rational number.

3√2=a/b,where a and b are co-prime integers,b≠0.

√2=a/3b

√2 is a rational number.

(Since a,b and 3 are Integers=a/3b is a rational number).

This contradicts the fact that √2 is an irrational number.

so ,our assumption was wrong .

Hence , 3√2 is an irrational number.

Answer 2

Answer:

let :-

$3 \sqrt{2}$

$3 \sqrt{2 } = \frac{a}{b}$

$3 \sqrt{2 } = \frac{a}{3b}$

• L.H.S. is irrational number.

• R.H.S is rational number.

• R.H.S. so, supposition is wrong.

• $3 \sqrt{2} \: \: is \: rational \: \: number$