State whether the following statement is true:
There is a number $x$ such that $x^{2}$ is irrational but $x^{4}$ is rational. Justify your answer by an example.

(TRUE) The statement is true.
Let us consider $x = \sqrt[4]{2}$.
Now,calculate $x^{2}$:
$x^{2} = (\sqrt[4]{2})^{2} = \sqrt{2}$. Since $\sqrt{2}$ cannot be expressed as a ratio of two integers,it is an irrational number.
Next,calculate $x^{4}$:
$x^{4} = (\sqrt[4]{2})^{4} = 2$. Since $2$ can be expressed as $\frac{2}{1}$,it is a rational number.
Thus,we have found a number $x = \sqrt[4]{2}$ such that $x^{2}$ is irrational and $x^{4}$ is rational.