Use the product rule to rewrite the term inside the radical as a product, then simplify.
$\sqrt{180}$

• A. $2\sqrt{20}$
• B. $6\sqrt{5}$
• C. $2\sqrt{45}$
• D. $36\sqrt{5}$

Answer: (B)

Verified step by step guidance

1. 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.
2. 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}$.
3. Use the product rule for square roots, which states that \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\). Apply this to get \(\sqrt{36} \times \sqrt{5}\).
4. Simplify \(\sqrt{36}\) since 36 is a perfect square. This simplifies to 6, so the expression becomes \$6 \times \sqrt{5}$.
5. Write the final simplified form as \$6\sqrt{5}\(, which is the simplified radical expression equivalent to \)\sqrt{180}$.