2.2.3 Squares, Square Roots, Cube and Cube Roots, PT3 Practice

Question 10:

\begin{array}{l} (a) Find the value of \sqrt{0.09} \\ (b) Calculate the value of {(\frac{5}{7} \times \sqrt{49})}^{2} \end{array}

Solution:

\begin{array}{l} (a) \\ \sqrt{0.09} = \sqrt{\frac{9}{100}} = \frac{3}{10} = 0.3 \\ (b) \\ {(\frac{5}{7} \times \sqrt{49})}^{2} = {(\frac{5}{7} \times 7)}^{2} \\ = 5^{2} \\ = 25 \end{array}

Question 11:

\begin{array}{l} (a) Find the value of \sqrt[3]{- \frac{1}{27}} \\ (b) Calculate the value of {(7 + \sqrt[3]{- 8})}^{2} \end{array}

Solution:

\begin{array}{l} (a) \\ \sqrt[3]{- \frac{1}{27}} = \sqrt[3]{- \frac{1}{3} \times - \frac{1}{3} \times - \frac{1}{3}} = - \frac{1}{3} \\ (b) \\ {(7 + \sqrt[3]{- 8})}^{2} = {[7 + (- 2)]}^{2} \\ = 5^{2} \\ = 25 \end{array}

Question 12:

\begin{array}{l} (a) Find the value of {(- \frac{1}{4})}^{3} . \\ (b) Calculate the value of {(4.2 \div \sqrt[3]{27})}^{2} . \end{array}

Solution:

\begin{array}{l} (a) \\ {(- \frac{1}{4})}^{3} = - \frac{1}{4} \times - \frac{1}{4} \times - \frac{1}{4} \\ = - \frac{1}{64} \\ (b) \\ {(4.2 \div \sqrt[3]{27})}^{2} = {(4.2 \div 3)}^{2} \\ = {1.4}^{2} \\ = 1.4 \times 1.4 \\ = 1.96 \end{array}

Question 13:

\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{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{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{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}