Question

privet root 3 + root 5 is irrational

Answer 1

Let √3+√5 be a rational number.

A rational number can be written in the form of p/q.

√3+√5 = p/q

Squaring on both sides,

(√3+√5)² = (p/q)²

(√3²+√5²+2(√3)(√5)) = p²/q²

3+5+2√15 = p²/q²

8+2√15 = p²/q²

2√15 = p²/q²-8

2√15 = (p²-8q²)/q²

√15 = (p²-8q²)2q²

p,q are integers then (p²-8q²)/2q² is a rational number.

Then √15 is also a rational number.

But this contradicts the fact that √15 is an irrational number.

So our supposition is false.

Therefore,√3+√5 is an irrational number.

Hence proved.

Hope it helps …