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 to simplify: \(\sqrt{\frac{x^2}{36}}\).
2. Recall the quotient rule for square roots, which states 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. Combine the simplified parts to get \(\frac{|x|}{6}\). Since \(x\) is typically considered nonnegative in this context, you can write this as \(\frac{x}{6}\).
5. Thus, the simplified form of the original expression is \(\frac{x}{6}\).