Question

prove that √5 - √3 is not a rational number ​

Answer 1

Step-by-step explanation:

let assume that √5-√3 is irrational

then ,there exist co prime a and b such that b is not equal to zero.

√5-√3 = a/b

√5 = a/b+√3

squaring on both sides

(√5)2 = (a/b +√3)2

5 = (a/b)2 + (√3)2 +2*a/b*√3

3a/b√3 =(a)2/ (b)2-1

√3 = (a)2-(b)2/3ab

since a and b are integer so (a)2-(b)2/3ab is irrational

thus √3 is also rational

But this contradiction fact that √2 is irrational so our assumption is incorrect

hence √5 -√3 is irrational