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Give the value for each. Round to the nearest 100th if necessary. root(3)((8)/(216))

Give the value for each. Round to the nearest 100100th if necessary.\newline82163 \sqrt[3]{\frac{8}{216}}

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Full solution

Q. Give the value for each. Round to the nearest 100100th if necessary.\newline82163 \sqrt[3]{\frac{8}{216}}
  1. Calculate Cube Roots: Calculate the cube root of the numerator and denominator separately. \newline83=2\sqrt[3]{8} = 2 because 23=82^3 = 8.\newline2163=6\sqrt[3]{216} = 6 because 63=2166^3 = 216.
  2. Divide Cube Roots: Divide the cube roots to get the final answer. 26=13\frac{2}{6} = \frac{1}{3}.
  3. Round to Nearest Hundredth: Since the problem asks to round to the nearest hundredth if necessary, we convert 13\frac{1}{3} to a decimal.\newline13=0.333...\frac{1}{3} = 0.333...\newlineRounded to the nearest hundredth is 0.330.33.

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