Question

If 1/x = x^2/27, then find x. Is it a rational or irrational number?

Answer 1

x cube will be 27
so x is 3..rational

Answer 2

1/x = x2/27
=> 27 = x2 * x                 (on cross multiplication)
=> 27 = x2 + 1                (powers add up when same bases are multiplied to each other)
=> 27 = x3
=> 3√27 = x                  (Here 3√ means cube root)
=> 3= x 
As you can see, 3 is a rational number, therefore x is a rational number