Use the quotient rule to simplify.
$\sqrt{\frac{x^2}{36}}$

• A. $\frac{\sqrt{x}}{36}$
• B. $\frac{x}{6}$
• C. $\frac{\sqrt{x}}{6}$
• D. $\frac{x^2}{6}$

Answer: (B)

Verified step by step guidance

1. Start with the expression under the square root: \(\sqrt{\frac{x^2}{36}}\).
2. Recall the property of square roots that \(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\). Apply this to rewrite the expression as \(\frac{\sqrt{x^2}}{\sqrt{36}}\).
3. Simplify the square roots separately: \(\sqrt{x^2}\) simplifies to \(|x|\) (the absolute value of \(x\)), and \(\sqrt{36}\) simplifies to \(6\).
4. Rewrite the expression as \(\frac{|x|}{6}\).
5. If the context allows (for example, if \(x\) is nonnegative), you can simplify \(|x|\) to \(x\), resulting in \(\frac{x}{6}\).