Question

prove that √2-3√3 is irrational number​

Answer 1

Step-by-step explanation:

let √2-2√3 be a rational no.

so let √2-2√3 = m

√2 = m - 2√3

(√2)² = (m - 2√3)²

2= m² + 12- 4√3m

4√3m = m²  -10

√3=  (m²  -10)÷4m

as m is rational and m≠0

so, (m²  -10)÷4m is rational

but √3 is rational

this contradict our assumption that √3 is irrational

• therefore, √2-3√3 is an irrational number