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