Question

Prove That
$\sqrt{5} + 2$
is irrational ​

Answer 1

we will prove that √5 is irrational number
then whole term will be √5+2 is irrational number

Answer 2

Solution :

We can only  Solve this Question by Contradiction Method . We have Given √5 + 2 and We need to Prove it irrational

Let √5 + 2 be a rational Number

It means it can be Written in the form of P/Q Where P and Q are Co-Prime ( No other factor except one )

√5 + 2 = (a/b)

⇒ √5 = (a/b) - 2

⇒ √5 = (a - 2b)/(b)

Here , √5  is an irrational number but (a - 2b)/(b) is a rational number

Since , Rational is not equal to irrational

Our assumption is incorrect!

Hence , √5 + 2 is an irrational number

Hence , Proved