Question

Prove that √3 is an irrational number . Hence show that 3 + 2 √ 3

is also an irrational number​

Answer 1

If possible, Let (3 + 2 √ 3) be a rational number.

⟹3 - (3 + 2 √ 3) is a rational.

∴ (2 √ 3) is a rational.

This contradicts the fact that (2 √ 3) is an irrational number.

Since, the contradiction arises by assuming (3+2√ 3) is a rational.

Hence, (3 + 2 √ 3) is irrational.

Proved.