Question

Maths problem
√5-3√2 is irrational number prove it
Please solve the answer help me

Answer 1

Let √5 - 3√2 be a rational number.

•°•

√5 - 3√2 = a / b

√5 = ( a / b ) + 3√2

√5 = ( a + 3√2 ) / b

Squaring both sides, we get

( √5 )² = [ ( a + 3√2 ) / b ]²

5 = ( a + 3√2 )² / b²

On right - Hand side, if we solve, the answer come will be an irrational number. But on left hand side, 5 is a rational number.

Hence, our contradiction was wrong.

Therefore, √5 - 3√2 is an irrational number.