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Simplifying $\sqrt{63u^3v^5}$

Example

Simplifying $\sqrt{98a^7b^5}$

Simplify the square root $\sqrt{98a^7b^5}$ by extracting the largest perfect square factors. For the coefficient $98$ , the largest perfect square factor is $49$ . For the variables $a^7$ and $b^5$ , the largest even powers are $a^6$ and $b^4$ . Rewrite the expression as the product of the perfect square $49a^6b^4$ and the remaining factors $2ab$ :

$\sqrt{49a^6b^4 \cdot 2ab}$

Apply the Product Property to separate the radicals: $\sqrt{49a^6b^4} \cdot \sqrt{2ab}$ . Simplify the perfect square root: $\sqrt{49} = 7$ , $\sqrt{a^6} = |a^3|$ , and $\sqrt{b^4} = b^2$ . Multiply this by the remaining radical to obtain the final simplified form $7|a^3|b^2\sqrt{2ab}$ .

Updated 2026-05-01

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OpenStax Intermediate Algebra

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