Example

Simplifying 98\sqrt{98}

Simplify the square root 98\sqrt{98} using the Product Property of Roots. First, find the largest factor in the radicand that is a perfect square. The largest perfect square factor of 9898 is 4949. Rewrite the radicand as a product of two factors: 98=492\sqrt{98} = \sqrt{49 \cdot 2}. Second, use the product rule to rewrite the radical as the product of two radicals: 492\sqrt{49} \cdot \sqrt{2}. Third, simplify the root of the perfect power. Since 49=7\sqrt{49} = 7, the expression becomes 727\sqrt{2}. When writing the simplified form, always write the integer in front of the square root so that it is not confused with the index.

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Updated 2026-05-01

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