Prove that `1/(2-sqrt(5))` is an irrational number.

prove that (1)/(3-2sqrt(5)) is an irrational number.

Prove that (1)/(sqrt(2)) is an irrational number.

Prove that sqrt(3)-sqrt(5) is an irrational number.

Prove that 2-3sqrt(5) is an irrational number.

Prove that 2-3sqrt(5) is an irrational number.

Prove that 2-3sqrt(5) is an irrational number.

Prove that sqrt(3)+sqrt(5) is an irrational number.

Prove that (2sqrt3+sqrt5) is an irrational number. Also check whether (2sqrt 3+ sqrt5)(2sqrt 3- sqrt5) is rational or irrational.

Prove that (2sqrt3+sqrt5) is an irrational number. Also check whether (2sqrt 3+ sqrt5)(2sqrt 3- sqrt5) is rational or irrational.

Prove that (2sqrt3+sqrt5) is an irrational number. Also check whether (2sqrt 3+ sqrt5)(2sqrt 3- sqrt5) is rational or irrational.