Use the quotient rule to divide, then simplify.
$\frac{\sqrt{75}}{\sqrt{3}}$

• A. $5$
• B. $3\sqrt{5}$
• C. $\sqrt{5}$
• D. $5\sqrt{3}$

Answer: (A)

Verified step by step guidance

1. Start with the given expression: \(\frac{\sqrt{75}}{\sqrt{3}}\).
2. Use the quotient rule for square roots, which states that \(\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}\). Apply this to rewrite the expression as \(\sqrt{\frac{75}{3}}\).
3. Simplify the fraction inside the square root: \(\frac{75}{3} = 25\), so the expression becomes \(\sqrt{25}\).
4. Recognize that \(\sqrt{25}\) is a perfect square, which simplifies to 5.
5. Therefore, the simplified form of the original expression is 5.