Question

no one by root 5 minus root 3 is irrational

Answer 1

yes it is irrational

Answer 2

Hey frnd...
Let -√3+√5 be a rational number.
A rational number can be written in the form of p/q where p,q are integers.
-√3+√5 = p/q
-√3 = p/q-√5

Squaring on both sides,
(-√3)² = (p/q-√5)²
3 = p²/q²+√5²-2(p/q)(√5)
√5×2p/q = p²/q²+5-3
√5 = (p²+2q²)/q² × q/2p
√5 = (p²+2q²)/2pq

p,q are integers then (p²+2q²)/2pq is a rational number.
Then √5 is also a rational number.
But this contradicts the fact that √5 is an irrational number.
So,our supposition is false.
Therefore, -√3+√5 is an irrational number.
Hope helps