Simplify the following.
$\sqrt{\frac{9}{x^2}}$

• A. $\(\frac{3}{x}\)$
• B. $\(\frac\)13$
• C. $\(\frac{9}{x}\)$
• D. $\(\frac{3}{x^2}\)$

Answer: (A)

Verified step by step guidance

1. Start with the expression under the square root: \(\sqrt{\frac{9}{x^2}}\).
2. Recall that the square root of a fraction can be written as the fraction of the square roots: \(\sqrt{\frac{9}{x^2}} = \frac{\sqrt{9}}{\sqrt{x^2}}\).
3. Simplify the square root of the numerator: \(\sqrt{9} = 3\).
4. Simplify the square root of the denominator: \(\sqrt{x^2} = |x|\) (the absolute value of \(x\)), but if \(x\) is positive, this simplifies to \(x\).
5. Combine the simplified numerator and denominator to write the expression as \(\frac{3}{x}\).