Multiple Choice
Use the quotient rule to simplify.
11. Roots, Radicals, and Complex Numbers
Simplifying Radical Expressions
Multiple Choice
Simplify the following.
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Verified step by step guidance1
Recognize that the expression to simplify is the square root of a product: \(\sqrt{49m^2}\). This means you are finding the square root of both 49 and \(m^2\) together.
Recall the property of square roots that \(\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}\). Apply this to separate the square root into two parts: \(\sqrt{49} \cdot \sqrt{m^2}\).
Simplify \(\sqrt{49}\) by identifying that 49 is a perfect square, so \(\sqrt{49} = 7\).
Simplify \(\sqrt{m^2}\) by using the rule that the square root of a variable squared is the absolute value of the variable, so \(\sqrt{m^2} = |m|\). Since we usually assume \(m\) is non-negative in algebra problems unless stated otherwise, this simplifies to \(m\).
Combine the simplified parts to write the final simplified expression as \$7m$.
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