Question

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

Answer 1

Answer:

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.