3.2.4 Squares, Square Roots, Cube and Cube Roots, PT3 Practice - Mathematics

Question 13:

\begin{matrix} (a) Find the value of \sqrt[3]{0.008} . (b) Calculate the value of 3^{2} \times \sqrt[3]{- \frac{64}{27}} . \end{matrix}

$\begin{array}{l} (a) Find the value of \sqrt[3]{0.008} . \\ (b) Calculate the value of 3^{2} \times \sqrt[3]{- \frac{64}{27}} . \end{array}$

Solution:

\begin{matrix} (a) \sqrt[3]{0.008} = \sqrt[3]{\frac{8}{1000}} = \frac{2}{10} = 0.2 (b) 3^{2} \times \sqrt[3]{- \frac{64}{27}} = 9^{3} \times - \frac{4}{3} = 12 \end{matrix}

$\begin{array}{l} (a) \\ \sqrt[3]{0.008} = \sqrt[3]{\frac{8}{1000}} \\ = \frac{2}{10} \\ = 0.2 \\ (b) \\ 3^{2} \times \sqrt[3]{- \frac{64}{27}} = 9^{3} \times - \frac{4}{3} \\ = 12 \end{array}$

Question 14:

\begin{matrix} (a) Find the value of {(- \frac{3}{4})}^{3} . (b) Calculate the value of \sqrt[3]{2 \frac{10}{27}} \div (2^{2} - 3^{2}) . \end{matrix}

$\begin{array}{l} (a) Find the value of {(- \frac{3}{4})}^{3} . \\ (b) Calculate the value of \sqrt[3]{2 \frac{10}{27}} \div (2^{2} - 3^{2}) . \end{array}$

Solution:

\begin{matrix} (a) {(- \frac{3}{4})}^{3} = - \frac{3}{4} \times - \frac{3}{4} \times - \frac{3}{4} = - \frac{27}{64} (b) \sqrt[3]{2 \frac{10}{27}} \div (2^{2} - 3^{2}) = \sqrt[3]{\frac{64}{27}} \div (4 - 9) = \frac{4}{3} \div - 5 = \frac{4}{3} \times - \frac{1}{5} = - \frac{4}{15} \end{matrix}

$\begin{array}{l} (a) \\ {(- \frac{3}{4})}^{3} = - \frac{3}{4} \times - \frac{3}{4} \times - \frac{3}{4} \\ = - \frac{27}{64} \\ (b) \\ \sqrt[3]{2 \frac{10}{27}} \div (2^{2} - 3^{2}) = \sqrt[3]{\frac{64}{27}} \div (4 - 9) \\ = \frac{4}{3} \div - 5 \\ = \frac{4}{3} \times - \frac{1}{5} \\ = - \frac{4}{15} \end{array}$

Question 15:
Match each of the following with the correct value.

Solution:

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