Prove that `( 5-2 sqrt3) is an irrraional number.

prove that (2 sqrt3 -1) is an irrational number.

Prove that ( 4-5 sqrt2) is an irrational number.

Prove that ( 4-5 sqrt2) is an irrational number.

Prove that 5-3/7 sqrt(3) is an irrational number.

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

Prove that 2 + 5 sqrt(3) is an irrational number, given that sqrt(3) is an irrational number

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

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

Prove that 5-sqrt(3) 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.