Give an example of a number x such that x2 is an irrational number and x3 is a rational number.

The cube roots of natural numbers which are not perfect cubes are all irrational numbers.

Let $x=\sqrt[3]{2}=2^{\frac{1}{3}}$

Now,

$x^{2}=\left(2^{\frac{1}{3}}\right)^{2}=2^{\frac{2}{3}}=\left(2^{2}\right)^{\frac{1}{3}}=4^{\frac{1}{3}}$, which is an irrational number

Also,

$x^{3}=\left(2^{\frac{1}{3}}\right)^{3}=2^{3 \times \frac{1}{3}}=2$, which is a rational number