Question

Prove that 8-√2is irrational number

Answer 1

ANSWER:

• (8-√2) is an irrational number.

GIVEN:

• Number = 8-√2

TO PROVE:

• 8-√2 is an Irrational number.

SOLUTION:

$\implies \: 8 - \sqrt{2} = \dfrac{p}{q} \\ \\ \implies \: 8 - \dfrac{p}{q} = \sqrt{2} \\ \\ \implies \: \ \dfrac{8q - p}{q} = \sqrt{2}$

Here:

• (8q-p)/q is rational but √2 is Irrational.
• Thus our contradiction is wrong.
• (8-√2) is an irrational number.

NOTE:

• This method of proving and irrational number is called contradiction method.