Multiple Choice
Use the product rule to rewrite the term inside the radical as a product, then simplify.
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9. Roots, Radicals, and Complex Numbers
Simplifying Radical Expressions
Multiple Choice
Use the quotient rule to simplify.
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Verified step by step guidance1
Recognize that the expression \( \sqrt[3]{\frac{t}{8}} \) is a cube root of a fraction, which can be rewritten using the property of radicals: \( \sqrt[3]{\frac{a}{b}} = \frac{\sqrt[3]{a}}{\sqrt[3]{b}} \).
Apply this property to rewrite the expression as \( \frac{\sqrt[3]{t}}{\sqrt[3]{8}} \).
Recall that \( \sqrt[3]{8} \) is the cube root of 8, which simplifies to a number since 8 is a perfect cube.
Replace \( \sqrt[3]{8} \) with its simplified value to get \( \frac{\sqrt[3]{t}}{\text{simplified value}} \).
Write the final simplified expression as a fraction with \( \sqrt[3]{t} \) in the numerator and the simplified cube root of 8 in the denominator.
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