Prove that `sqrt2+sqrt2` is irrational .

(i) Prove that sqrt2 is an irrational number. (ii) Prove that sqrt3 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.

Show that sqrt2 is irrational.

Prove that sqrt5 is irrational, (use the method of contradiction).

Prove that sqrt3 is irrational, (use the method of contradiction)

Show that 3sqrt2 is irrational.

Show that 5-sqrt3 is irrational.

Define a rational number and prove that sqrt(2) is not rational.

Prove that sqrt2 irrational, (use the method of contradiction).

Verify by the method of contradiction that sqrt7 is irrational.