how to prove √(√2+√3) is irrational?

Suppose to the contrary that x = √(√2+√3) were rational.

Squaring both sides:
x^2 = √2+√3.

Squaring both sides again:
x^4 = 5 + 2√6
==> √6 = (x^4 - 5)/2.

Since x is assumed rational, it follows via closure axioms of the set of rational numbers that (x^4 - 5)/2 is also rational.

This is a contradiction, because √6 is irrational (which can be proved in the same manner that √2 is irrational).

Therefore, √(√2+√3) is irrational.

I hope this helps!

Bc the answer would come out to be the sq root of 5 which is an odd number. And you can't have a odd number under a sq rt as the answer