Scelta multipla
Use the product rule to multiply the following.
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11. Roots, Radicals, and Complex Numbers
Simplifying Radical Expressions
Scelta multipla
Use the quotient rule to simplify.
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Start with the expression to simplify: \(\sqrt{\frac{x^2}{36}}\).
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 \(\frac{\sqrt{x^2}}{\sqrt{36}}\).
Simplify the square roots separately: \(\sqrt{x^2}\) simplifies to \(|x|\) (the absolute value of \(x\)), and \(\sqrt{36}\) simplifies to \(6\).
Combine the simplified parts to get \(\frac{|x|}{6}\). Since \(x\) is typically considered nonnegative in this context, you can write this as \(\frac{x}{6}\).
Thus, the simplified form of the original expression is \(\frac{x}{6}\).
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