Example

Simplifying 7548\sqrt{\frac{75}{48}}

Practice simplifying a square root whose radicand is a fraction that can be reduced to a perfect square fraction. For example, to simplify 7548\sqrt{\frac{75}{48}}:

Simplify inside the radical first. Rewrite the numerator and denominator showing their common factors: 325316\sqrt{\frac{3 \cdot 25}{3 \cdot 16}}.

Remove the common factor of 33: 2516\sqrt{\frac{25}{16}}.

The reduced fraction is a perfect square fraction, since (54)2=2516\left(\frac{5}{4}\right)^2 = \frac{25}{16}. Therefore, the simplified result is 54\frac{5}{4}.

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Updated 2026-05-01

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