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Give the value for each. Round to the nearest 100th if necessary.

root(3)((9)/(125))

Give the value for each. Round to the nearest $100$ th if necessary. $\newline$ $\sqrt[3]{\frac{9}{125}}$

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Roots of rational numbers

Full solution

Q. Give the value for each. Round to the nearest

100

th if necessary.

\newline

\sqrt[3]{\frac{9}{125}}

Calculate Cube Root Separately: Calculate the cube root of the numerator and denominator separately. $\sqrt[3]{9} = \sqrt[3]{3 \times 3} = 3^{\frac{2}{3}}$
Calculate Denominator Cube Root: Calculate the cube root of the denominator. $\sqrt[3]{125} = \sqrt[3]{5 \times 5 \times 5} = 5$
Divide Numerator by Denominator: Divide the cube root of the numerator by the cube root of the denominator. $\newline$ $\frac{3^{\frac{2}{3}}}{5}$
Find Decimal Value: Use a calculator to find the decimal value of $3^{\frac{2}{3}}$ . $\newline$ $3^{\frac{2}{3}} \approx 2.08$
Divide and Round: Divide the decimal value by $5$ and round to the nearest hundredth if necessary. $\newline$ $2.08 / 5 \approx 0.42$

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