Question

prove that √2 + √3 is an irrational no

Answer 1

Heya!

Here is yr answer......


Let us assume √2+√3 is rational

let √2+√3 = a/b [ a, b are any two integers]


=> √3 = a/b-√2

by squaring on both sides......

=> 9 = a²/b²+2-2(a/b)(√2)

=> 9 = a²/b²+2-2√2a/b

=> 2√2a/b = a²/b²+2-9

=> 2√2a/b = a²/b²-7

=> 2√2a/b = a²-7b²/b²

=> 2√2a = a²-7b²/b

=> √2 = a²-7b²/2ab


For any two integers RHS (a²-7b²/2ab) is rational

But, LHS(√2) is irrational.

A rational and irrational are never equal.!

So, assumption is false

Therefore, √2+√3 is irrational


Hope it hlpz..