Multiple Choice
Use the quotient rule to simplify.
9. Roots, Radicals, and Complex Numbers
Simplifying Radical Expressions
Multiple Choice
Simplify the following.
A
B
C
D
Verified step by step guidance1
Start with the expression under the square root: \(\sqrt{\frac{9}{x^2}}\).
Recall the property of square roots that \(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\), so rewrite the expression as \(\frac{\sqrt{9}}{\sqrt{x^2}}\).
Simplify the square root of the numerator: \(\sqrt{9}\) is a perfect square, so it simplifies to 3.
Simplify the square root of the denominator: \(\sqrt{x^2}\) simplifies to the absolute value of \(x\), which is \(|x|\), but if \(x\) is positive, it simplifies to \(x\).
Combine the simplified numerator and denominator to write the expression as \(\frac{3}{x}\) (assuming \(x > 0\)).
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