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Definition

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, 964\frac{9}{64} is a perfect square fraction because the numerator 9=329 = 3^2 and the denominator 64=8264 = 8^2 are both perfect squares. Similarly, 2516\frac{25}{16} and 4981\frac{49}{81} 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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Updated 2026-05-01

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