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Perfect Square Fraction
A perfect square fraction is a fraction in which both the numerator and the denominator are perfect squares. Because each part of the fraction is a perfect square, the square root of the entire fraction can be evaluated exactly — the square root of the numerator becomes the new numerator, and the square root of the denominator becomes the new denominator.
For example, is a perfect square fraction because the numerator and the denominator are both perfect squares. Similarly, and are perfect square fractions.
When simplifying a square root, the first step is always to determine whether the radicand is a perfect square. If the radicand is a fraction, check whether both the numerator and denominator are perfect squares. If so, the fraction is a perfect square fraction and the square root simplifies directly. If the numerator and denominator share common factors, removing those common factors first may reveal a perfect square fraction underneath.
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