1Cademy - Simplifying $$\frac{4

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Simplifying $\frac{6 - \sqrt{24}}{12}$

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Simplifying $\frac{4 - \sqrt{48}}{2}$

To simplify a fraction with a radical in the numerator, such as $\frac{4 - \sqrt{48}}{2}$ , follow these steps: Step 1 — Simplify the radical. Rewrite the radicand using its largest perfect square factor: $\sqrt{48} = \sqrt{16 \cdot 3}$ . Rewrite as the product of two radicals and simplify: $\sqrt{16} \cdot \sqrt{3} = 4\sqrt{3}$ . The fraction becomes $\frac{4 - 4\sqrt{3}}{2}$ . Step 2 — Factor the common factor from the numerator. Both terms in the numerator share a factor of $4$ . Factoring it out gives $\frac{4(1 - \sqrt{3})}{2}$ . Step 3 — Remove the common factor. Cancel the common factor of $2$ from the numerator and the denominator: $\frac{2 \cdot 2(1 - \sqrt{3})}{2}$ . The simplified result is $2(1 - \sqrt{3})$ . Remember that to simplify a fraction, a common factor must be factored out from the entire numerator before canceling with the denominator.

Updated 2026-05-01

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OpenStax Intermediate Algebra

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