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.
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,
Let us take $x=\sqrt[4]{2}$
Now, $\quad x^{2}=(\sqrt[4]{2})^{2}=\sqrt{2},$ an irrational number.
$x^{4}=(\sqrt[4]{2})^{4}=2,$ a rational number.
So, we have a number $x$ such that $x^{2}$ is irrational but $x^{4}$ is rational.
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