**Question 10:**$\begin{array}{l}\text{(a)Findthevalueof}\sqrt{0.09}\\ \text{(b)Calculatethevalueof}{\left(\frac{5}{7}\times \sqrt{49}\right)}^{2}\end{array}$

*Solution*:$\begin{array}{l}\text{(a)}\\ \sqrt{0.09}=\sqrt{\frac{9}{100}}=\frac{3}{10}=0.3\\ \\ \text{(b)}\\ {\left(\frac{5}{7}\times \sqrt{49}\right)}^{2}={\left(\frac{5}{\overline{)7}}\times \overline{)7}\right)}^{2}\\ \text{}={5}^{2}\\ \text{}=25\end{array}$

**Question 11:**$\begin{array}{l}\text{(a)Findthevalueof}\sqrt[3]{-\frac{1}{27}}\\ \text{(b)Calculatethevalueof}{\left(7+\sqrt[3]{-8}\right)}^{2}\end{array}$

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

**Question 12:**$\begin{array}{l}\text{(a)Findthevalueof}{\left(-\frac{1}{4}\right)}^{3}.\\ \text{(b)Calculatethevalueof}{\left(4.2\xf7\sqrt[3]{27}\right)}^{2}.\end{array}$

*Solution*:$\begin{array}{l}\text{(a)}\\ {\left(-\frac{1}{4}\right)}^{3}=-\frac{1}{4}\times -\frac{1}{4}\times -\frac{1}{4}\\ \text{}=-\frac{1}{64}\\ \\ \text{(b)}\\ {\left(4.2\xf7\sqrt[3]{27}\right)}^{2}={\left(4.2\xf73\right)}^{2}\\ \text{}={1.4}^{2}\\ \text{}=1.4\times 1.4\\ \text{}=1.96\end{array}$

**Question 13:**$\begin{array}{l}\text{(a)Findthevalueof}\sqrt[3]{0.008}.\\ \text{(b)Calculatethevalueof}{3}^{2}\times \sqrt[3]{-\frac{64}{27}}.\end{array}$

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

**Question 14:**$\begin{array}{l}\text{(a)Findthevalueof}{\left(-\frac{3}{4}\right)}^{3}.\\ \text{(b)Calculatethevalueof}\sqrt[3]{2\frac{10}{27}}\xf7\left({2}^{2}-{3}^{2}\right).\end{array}$

*Solution*:$\begin{array}{l}\text{(a)}\\ {\left(-\frac{3}{4}\right)}^{3}=-\frac{3}{4}\times -\frac{3}{4}\times -\frac{3}{4}\\ \text{}=-\frac{27}{64}\\ \\ \text{(b)}\\ \sqrt[3]{2\frac{10}{27}}\xf7\left({2}^{2}-{3}^{2}\right)=\sqrt[3]{\frac{64}{27}}\xf7\left(4-9\right)\\ \text{}=\frac{4}{3}\xf7-5\\ \text{}=\frac{4}{3}\times -\frac{1}{5}\\ \text{}=-\frac{4}{15}\end{array}$