Example

Simplifying 45\sqrt{45}

Simplify the square root 45\sqrt{45} 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 4545 is 99. Rewrite the radicand as a product of two factors: 45=95\sqrt{45} = \sqrt{9 \cdot 5}. Second, use the product rule to rewrite the radical as the product of two radicals: 95\sqrt{9} \cdot \sqrt{5}. Third, simplify the root of the perfect power. Since 9=3\sqrt{9} = 3, the simplified expression is 353\sqrt{5}.

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Updated 2026-05-01

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