Question

Given that
$\sqrt{5}$
is irrational, prove that 2V5 -3 is an irrational number.​

Answer 1

We have to prove that 2√5-3 is irrational...

let us assume that 2√5-3 is rational

therefore,

2√5-3=a/b {where a and b are co-primes}

2√5=a/b+3

2√5=a+3b/b

√5=a+3b/2b

Hence, RHS is rational so. LHS i.e √5 well also rational....

But it contradicts the fact that √5 is rational.This contradiction arised due to our wrong assumption.

Therefore our assumption was wrong and 2√5-3 is an irrational number....

*HENCE PROVED*

Step-by-step explanation:

plz mark me as best