If `x=3+2sqrt(2),` check whether `x+1/x` is rational or irrational.

If x=3+sqrt2 then find whether x-1/x and x^2+1/x^2 is rational or irrational

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

Check whether x+3 is irrational numbers or not?

Check whether 21+sqrt3 is irrational numbers or not?

Check whether 5sqrt2 is irrational numbers or not ?

Check whether 5/(sqrt2) is irrational numbers or not?

Check whether -sqrt63/sqrt448 is a rational number or 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.