Question

Prove that 3 + 2√2 is irrational.

Answer 1

ANSWER:

• 3+2√2 is an irrational number.

GIVEN:

• Number 3+2√2

TO PROVE:

• 3+2√2 is an Irrational number.

SOLUTION:

Let 3+2√2 be a rational number which can be expressed in the form of p/q where p and q have no common factor other than 1.

$\implies \: 3 + 2 \sqrt{2} = \dfrac{p}{q} \\ \\ \implies \: 2 \sqrt{2} = \dfrac{p}{q} - 3 \\ \\ \implies \: 2 \sqrt{2} = \dfrac{p - 3q}{q} \\ \\ \implies \: \sqrt{2} = \dfrac{p - 3q}{2q}$

Here:

• (p-3q)/2q is rational but √2 is Irrational .
• Thus our contradiction is wrong.
• 3+2√2 is an irrational number.

Answer 2

When a rational number and an irrational number adds,the sum is always irrational