Multiple Choice
Use the product rule to multiply the following.
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11. Roots, Radicals, and Complex Numbers
Simplifying Radical Expressions
Multiple Choice
Use the product rule to rewrite the term inside the radical as a product, then simplify.
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Verified step by step guidance1
Start with the expression inside the square root: \(\sqrt{180}\). The goal is to rewrite 180 as a product of two numbers, where one is a perfect square.
Find the largest perfect square factor of 180. Since \$36$ is a perfect square and divides 180 (because \(180 = 36 \times 5\)), rewrite the expression as \(\sqrt{36 \times 5}\).
Use the product rule for square roots, which states that \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\). Apply this to get \(\sqrt{36} \times \sqrt{5}\).
Simplify \(\sqrt{36}\) since 36 is a perfect square. This simplifies to 6, so the expression becomes \(6 \times \sqrt{5}\).
Write the final simplified form as \(6\sqrt{5}\), which is the simplified radical expression equivalent to \(\sqrt{180}\).
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