1Cademy - Simplifying $$\sqrt{98}$$

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How to Simplify a Square Root Using the Product Property

Example

Simplifying $\sqrt{98}$

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