Prove that `sqrt(2)+sqrt(3)` is irrational .

Prove that sqrt2+sqrt3 is irrational.

Prove that sqrt2+sqrt2 is irrational .

Prove that sqrt2-3sqrt5 is a irrational number.

Prove that (2sqrt3+sqrt5) is an irrational number. Also check whether (2sqrt3+sqrt5)(2sqrt3-sqrt5) is rational or irrational.

Prove that sqrt3 + sqrt5 is an irrational number.

Prove that sqrt2+sqrt11 is an irrational number.

Prove that sqrt3-sqrt5 is an irrational number.

Prove that sqrt3+sqrt7 is irrational.

Prove that sqrt5+sqrt11 is irrational.

Prove that sqrt5+sqrt7 is irrational.