Question

Prove that √7 + √2 is an irrational number, given that √14 is irrational number​

Answer 1

Answer:

let √7+√2 is a rational number and equal to X ( a rational number)

so X = √7+√2

squaring both side

X2= (√7+√2)2

X2= 7+2+2√14 {(a+b)2 = a2+b2+2ab}

(X2 - 9)/2= √14

we know that X is a rational number so (X2-9)/2 is also a rational number and equal to √14 so this is also a rational number but it is given that √14 it irradiation so our assumption is wrong .so √7+√2 is also irrational number.

hope helpful.........

thanks............