#### 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