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 given expression: \(\sqrt{\frac{x^2}{36}}\).
2. Recall that the square root of a fraction can be written as the fraction of the square roots: \(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\). Apply this to get \(\frac{\sqrt{x^2}}{\sqrt{36}}\).
3. Simplify the square roots separately: \(\sqrt{x^2} = |x|\) (the absolute value of \(x\)) and \(\sqrt{36} = 6\).
4. Rewrite the expression as \(\frac{|x|}{6}\). Since \(x\) is typically considered nonnegative in this context, you can simplify \(|x|\) to \(x\).
5. Thus, the simplified form of the original expression is \(\frac{x}{6}\).