Question

prove 2-root 3 is irrational given that root 3 is irrational ​

Answer 1

Answer:

Let's assume that 2 - √3 is a rational number.

Square of the rational number is always rational number.

But, (2 - √3)² = 5 - 4√3

Given: √3 is an irrational number.

But, when irrational number is added to a rational number it gives irrational number.

Hence, our assumption goes wrong.

Therefore, 2 - √3 is an irrational number.