Multiple Choice
Use the quotient rule to simplify.
11. Roots, Radicals, and Complex Numbers
Simplifying Radical Expressions
Multiple Choice
Simplify the following.
A
B
C
D
Verified step by step guidance1
Recognize that the expression is a square root of a fraction: \(\sqrt{\frac{9}{x^2}}\).
Use the property of square roots that \(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\) to 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 \(|x|\). For simplicity, if \(x\) is positive, this is just \(x\).
Combine the simplified numerator and denominator to write the expression as \(\frac{3}{x}\).
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