[" Theorem "1.4:sqrt(2)" is irrational."],[" Proof: Let us assume,to the contrary,that "sqrt(2)" is rational."]

Prove that: 2sqrt(3) - 4 is an irrational number, using the fact that sqrt(3) is an irrational number.

Proof that 3sqrt3 is an irrational number.

Prove that 2sqrt3-4 is an irrational number, using the fact that sqrt3 is an irrational number.

Prove that 2 sqrt3 - 4 is an irrational number , using the fact that sqrt3 is an irrational number .

Examine; Whether 3+2sqrt(2) is rational or irrational.

Assuming that sqrt(2) is irrational, show that 5+sqrt(2) 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.