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 by expressing the number inside the square root, 180, as a product of two factors, one of which is a perfect square. For example, write 180 as \$36 \times 5$ because 36 is a perfect square.
2. Use the product rule for square roots, which states that \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\). Apply this to rewrite \(\sqrt{180}\) as \(\sqrt{36 \times 5} = \sqrt{36} \times \sqrt{5}\).
3. Simplify the square root of the perfect square. Since \(\sqrt{36} = 6\), replace \(\sqrt{36}\) with 6 to get \$6 \times \sqrt{5}$.
4. Write the simplified expression as \$6\sqrt{5}\(, which is the simplified form of \)\sqrt{180}$.
5. Verify your simplification by checking that no further perfect square factors remain inside the radical and that the expression is fully simplified.