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Answer :
The expression \(\sqrt{\frac{1}{25}}\) simplifies to \(\frac{1}{5}\) since the square root of 1 is 1, and the square root of 25 is 5.
To write \(\sqrt{\frac{1}{25}}\) as a simplified fraction, we start by noting that the square root of a fraction is the square root of the numerator divided by the square root of the denominator. This is because \(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\). Therefore, \(\sqrt{\frac{1}{25}}\) becomes \(\frac{\sqrt{1}}{\sqrt{25}}\).
The square root of 1 is 1 since 1 multiplied by itself yields 1, and similarly, the square root of 25 is 5 since 5 multiplied by itself yields 25. Thus, we have \(\frac{1}{5}\). This fraction is already in its simplest form because 1 and 5 have no common factors other than 1, which means it cannot be simplified further.
So, \(\sqrt{\frac{1}{25}}\) as a simplified fraction is \(\frac{1}{5}\).
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