Question

question
determine if \\(\sqrt{53}\\) is rational or irrational and give a reason for your answer.
answer attempt 1 out of 2
the number \\(\sqrt{53}\\) is \\(\boxed{\text{irrational}}\\) because
(options: irrational, rational)
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Explanation:

A rational number can be written as $\frac{p}{q}$ where $p$ and $q$ are integers ($q
eq0$), and it corresponds to the square root of a perfect square. 53 is not a perfect square (the closest perfect squares are $7^2=49$ and $8^2=64$), so its square root cannot be expressed as a ratio of two integers.

Answer:

The number $\sqrt{53}$ is irrational because 53 is not a perfect square, so its square root cannot be written as a fraction of two integers.