Question

Prove that 2-3√5 is an irrational number.​

Answer 1

Let x=2−3
5
​
be a rational number.

3
5
​
=2−x

5
​
=
3
2−x
​


Since x is rational, 2-x is rational and hence
3
2−x
​
is also rational number

⇒
5
​
is a rational numbers, which is a contradiction.

Hence 2−3
5
​
must be an irrational number.

Answer 2

Step-by-step explanation:

To prove:-2-3√5 is an irrational no.

Let us assume contrary that 2-3√5 is rational.

Let 2-3√5 where a and b coprime numbers,

b is not Equal to 0

2-a/b=3√5

2b-a/3b=√5

Since a and b are integers ,we get 2b-a/3b is rational,so √5 is irrational .

But ,this condradicts the fact that √5 is irrational,the condradiction has arisen Because of our incorrect assumption that 2-3√5. is rational

So we conclude that 2-3√5 is irrational