Question

31. Prove that 2 - 3V5 is an irrational number.​

Answer 1

Answer:

Let 2- 3√5 be rational

Let 2- 3√5 be rationalthen, 2-3√5-2 (rational no. minus rational no. be a rational no.)

=(-3√5)

={-3√5÷(-3)} (rational no. divided by rational no. be a rational no.)

= √5

Then √5 is rational number

Then √5 is rational numberbut √5 is not a rational number

Then √5 is rational numberbut √5 is not a rational numberthus, it contaradicts our statement that the given equation is rational.

HENCE IT IS IRRATIONAL