Prove that `sqrt2 + sqrt7` is an irrational number.

Prove that sqrt3 + sqrt5 is an irrational number.

Prove that sqrt2+sqrt11 is an irrational number.

Prove that 2sqrt5+ sqrt7 is an Irrational Number. Also check whether (2sqrt5+sqrt7)(2sqrt5-sqrt7) a rational or Irrational.

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

Prove that sqrt2-3sqrt5 is a irrational number.

Prove that sqrt3-sqrt5 is an irrational number.

Show that sqrt5-sqrt3 is an irrational number.

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

Prove that sqrt3+sqrt7 is irrational.

Prove that sqrt5+sqrt7 is irrational.