Question

prove that 8- root 2 is irrational number?​

Answer 1

ANSWER:

• 8-√2 is an Irrational number.

GIVEN:

• Number = 8-√2

TO PROVE:

• 8-√2 is an Irrational number.

SOLUTION:

Let 8-√2 be a rational number which can be expressed in the form of p/q where p and q have no other common factor than 1.

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

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 an Irrational number is called contradiction method.
• In this method we first contradict a fact then we prove that our contradiction is wrong.

Answer 2

Answer:

yes 8 - root 2 is an irrational number