Multiple Choice
Simplify the root.
9. Roots, Radicals, and Complex Numbers
Introduction to Radical Expressions
Multiple Choice
Use a calculator to evaluate the following and round to the nearest hundredths.
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Verified step by step guidance1
Identify the expression to evaluate: the fifth root of 75, which can be written as \(\sqrt[5]{75}\) or equivalently \(75^{\frac{1}{5}}\).
Recall that the nth root of a number can be expressed as a fractional exponent: \(\sqrt[n]{a} = a^{\frac{1}{n}}\). So here, \(\sqrt[5]{75} = 75^{\frac{1}{5}}\).
Use a calculator to compute \(75^{\frac{1}{5}}\). This means raising 75 to the power of 0.2 (since \(\frac{1}{5} = 0.2\)).
After calculating the value, round the result to the nearest hundredths place. This means keeping two digits after the decimal point.
Write the rounded value as your final answer.
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