**2.2.2 Squares, Square Roots, Cube and Cube Roots, PT3 Focus Practice**

Question 6:

Question 6:

Complete the operation steps below by filling in the boxes using suitable numbers.

$\begin{array}{l}\sqrt[3]{4\frac{17}{27}}\xf7\sqrt{1\frac{9}{16}}=\sqrt[3]{\frac{\overline{)}}{27}}\xf7\sqrt{\frac{25}{16}}\\ \text{}=\frac{}{3}\xf7\frac{5}{4}\\ \text{}=\frac{}{3}\times \frac{4}{5}\\ \text{}=\overline{)}\end{array}$

$\begin{array}{l}\sqrt[3]{4\frac{17}{27}}\xf7\sqrt{1\frac{9}{16}}=\sqrt[3]{\frac{\overline{)}}{27}}\xf7\sqrt{\frac{25}{16}}\\ \text{}=\frac{}{3}\xf7\frac{5}{4}\\ \text{}=\frac{}{3}\times \frac{4}{5}\\ \text{}=\overline{)}\end{array}$

Solution:Solution:

$\begin{array}{l}\sqrt[3]{4\frac{17}{27}}\xf7\sqrt{1\frac{9}{16}}=\sqrt[3]{\frac{\overline{)125}}{27}}\xf7\sqrt{\frac{25}{16}}\\ \text{}=\frac{5}{3}\xf7\frac{5}{4}\\ \text{}=\frac{\overline{)5}}{3}\times \frac{4}{\overline{)5}}\\ \text{}=\overline{)\frac{4}{3}}\end{array}$

**Question 7:**

Complete the operation steps below by filling in the boxes using suitable numbers.

$\begin{array}{l}{\left(\sqrt{2\frac{7}{9}}-\sqrt[3]{\frac{27}{64}}\right)}^{2}={\left(\sqrt{\frac{\overline{)}}{9}}-\frac{3}{\overline{)}}\right)}^{2}\\ \text{}={\left(\frac{\overline{)}}{12}\right)}^{2}\\ \text{}=\overline{)}\end{array}$

Solution:Solution:

$\begin{array}{l}{\left(\sqrt{2\frac{7}{9}}-\sqrt[3]{\frac{27}{64}}\right)}^{2}={\left(\sqrt{\frac{\overline{)25}}{9}}-\frac{3}{\overline{)4}}\right)}^{2}\\ \text{}={\left(\frac{5}{3}-\frac{3}{4}\right)}^{2}\\ \text{}={\left(\frac{\left(5\times 4\right)-\left(3\times 3\right)}{12}\right)}^{2}\\ \text{}={\left(\frac{\overline{)11}}{12}\right)}^{2}\\ \text{}=\overline{)\frac{121}{144}}\end{array}$

**Question 8:**

Complete the operation steps below by filling in the boxes using suitable numbers.

$\begin{array}{l}\sqrt[3]{1\frac{61}{64}}-{0.3}^{2}=\sqrt[3]{\frac{\overline{)}}{64}}-{0.3}^{2}\\ \text{}=\frac{\overline{)}}{4}-\overline{)}\\ \text{}=\overline{)}\end{array}$

$\begin{array}{l}\sqrt[3]{1\frac{61}{64}}-{0.3}^{2}=\sqrt[3]{\frac{\overline{)}}{64}}-{0.3}^{2}\\ \text{}=\frac{\overline{)}}{4}-\overline{)}\\ \text{}=\overline{)}\end{array}$

Solution:Solution:

**Question 9:**

Find the value of:

$\begin{array}{l}\text{(a)}\sqrt[3]{\frac{10}{27}-5}\\ \text{(b)}\sqrt{\frac{4}{49}}\times \sqrt[3]{-0.216}\end{array}$

Solution:Solution:

$\begin{array}{l}\text{(a)}\sqrt[3]{\frac{10}{27}-5}=\sqrt[3]{\frac{10-135}{27}}\\ \text{}=\sqrt[3]{-\frac{125}{27}}\\ \text{}=-\frac{5}{3}\end{array}$

$\begin{array}{l}\text{(b)}\sqrt{\frac{4}{49}}\times \sqrt[3]{-0.216}=\frac{2}{7}\times \sqrt[3]{\frac{216}{1000}}\\ \text{}=\frac{\overline{)2}}{7}\times \frac{6}{5\overline{)10}}\\ \text{}=\frac{6}{35}\end{array}$