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

• A. $2\sqrt{20}$
• B. $6\sqrt5$
• C. $2\sqrt{45}$
• D. $36\sqrt5$

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, one of which is a perfect square.
2. Find the prime factorization of 180 or identify a perfect square factor. For example, 180 can be factored as \$36 \times 5$, where 36 is a perfect square.
3. Rewrite the square root using the product rule for radicals: \(\sqrt{180} = \sqrt{36 \times 5} = \sqrt{36} \times \sqrt{5}\).
4. Simplify the square root of the perfect square: \(\sqrt{36} = 6\), so the expression becomes \$6 \times \sqrt{5}$.
5. Write the simplified form as \$6\sqrt{5}$, which is the simplified radical expression.