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  • State whether the given statement is true or false? Justify your answer by an example. The square of an irrational number is always rational.

State whether the given statement is true or false? Justify your answer by an example. The square of an irrational number is always rational.

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Answer: False

Solution.

Any number which can be represented in the form of p/q where q is not equal to zero is a rational number.
Irrational numbers are real numbers which cannot be represented as simple fractions.
The given statement is: The square of an irrational number is always rational.
This is False, e.g., let us consider irrational numbers \sqrt{2} and 4\sqrt{2}
(a)(\sqrt{2})^{2}=2,which is a rational number.
(b)(4\sqrt{2})^{2}=\sqrt{2}, which is an irrational number.
Hence, square of an irrational number is not always a rational number.
Therefore the given statement is False.

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