Question

Prove that 5-root 3is iirational

Answer 1

ANSWER:

• (5-√3) is an Irrational number.

GIVEN:

• Number = (5-√3)

TO PROVE:

• (5-√3) is an Irrational number.

SOLUTION:

Let 5-√3 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.

$\implies \: 5 - \sqrt{3} = \dfrac{p}{q} \\ \\ \implies \: 5 - \dfrac{p}{q} = \sqrt{3} \\ \\ \implies \: \dfrac{5q - p}{q} = \sqrt{3}$

Here:

• (5q-p)/q is rational while √3 is an Irrational number.
• Thus our contradiction is wrong.
• (5-√3) is an Irrational number.