Question

prove √3+√2 is an irrational number​

Answer 1

Answer:

Prove that √(3) + √(2) is an irrational number.

Step-by-step explanation:

Let √3 - √2 = (a/b) is a rational no. So,5 - 2√6 = (a2/b2) a rational no. Since, 2√6 is an irrational no. ... So, (√3 - √2) is an irrational no.

Answer 2

Step-by-step explanation:

Let as assume that √2 + √3 is a rational number .

Then , there exists co - prime positive integers p and q such that

(√2+√3) = p/q

or, p/q –(√3) = (√2)

squaring on the both sides, we get

{(p/q) – √3}² = (√2)²

or, p²/q² – (2√3p)/q + 3 = 2

or, p²/q² +3 – 2 = (2√3p)/q

or, p²/q² + 1 = (2√3p)/q

or, (p²+q²)/q² = (2√3p)/q

or, (p²+q²)/2pq = √3. [Applying cross multiplication rule]

√3 is a irrational number. [pq are an Integers,

so (p²+q²)2pq is rational]

This contradicts the fact that √3 is irrational .

so assumption was incorrect . Here √2 + √3 is irrational.