Question :

Prove that √ 5 − √ 3 is not a rational number.Submitted on 21/1/2024 | Answered by Vandana Rana

Answer :

Let √5−√3 be a rational number of form a/b, where b≠0

Squaring on both sides
(√5−√3)²=(a/b)²
5+3 -2√15=a²/b²
√15 = (- a²/b² +8)/2
since √15 is irrational , (- a²/b²+8 )/2 is rational Since LHS ≠ RHS,
contradiction arises,

Therefore √5−√3 is irrational