Question

prove that √5 +√2 is irrational

Answer 1

Hi Friend !!!

Here is ur answer !!!

Let's assume that √5+√2 is a rational number

√5+√2 = p/q

√5 = p/q - √2

squaring on both sides

5 = p²/q² - 2(p/q)(√2) + 2

5-2 = p²/q²- 2p/q √2

p²/q² -3 = 2p/q √2

p²-3q²/q² (q/2p) = √2

p²-3q²/2pq = √2

if p, q are integers then p²-3q²/2pq is a rational number

Then √2 also a rational number

But it contradicts the fact that √2 is irrational number

So our assumption is wrong

√5 + √2 is an irrational number

Hope it helps u : )