Question
State whether the following statements are true or false? Justify your answer. The square of an irrational number is always rational.
✓
Answer
e.g., Let an irrational number be $\sqrt{2}$ and $\sqrt[4]{2}$
$a. (\sqrt{2})^2=2,$ which is a rational number.
$b. (\sqrt[4]{2})^2=\sqrt{2},$ which is not a rational number.
Hence, square of an irrational number is not always a rational number.
$a. (\sqrt{2})^2=2,$ which is a rational number.
$b. (\sqrt[4]{2})^2=\sqrt{2},$ which is not a rational number.
Hence, square of an irrational number is not always a rational number.
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