**2.2.1 Squares, Square Roots, Cube and Cube Roots, PT3 Practice 1**

Question 1:

Question 1:

Calculate the values of the following:

$\begin{array}{l}\text{(a)}\sqrt{\frac{50}{98}}\\ \text{(b)}\sqrt{1\frac{17}{64}}\\ \text{(c)}\sqrt{81}-\sqrt{0.01}\\ \text{(d)}\sqrt{3.24}\end{array}$

Solution:Solution:

$\text{(b)}\sqrt{1\frac{17}{64}}=\sqrt{\frac{81}{64}}=\frac{9}{8}=1\frac{1}{8}$

$\begin{array}{l}\text{(c)}\sqrt{81}-\sqrt{0.01}=9-\sqrt{\frac{1}{100}}\\ \text{}=9-\frac{1}{10}\\ \text{}=9-0.1\\ \text{}=8.9\end{array}$

$\begin{array}{l}\text{(d)}\sqrt{3.24}=\sqrt{3\frac{24}{100}}=\sqrt{3\frac{6}{25}}\\ \text{}=\sqrt{\frac{81}{25}}\\ \text{}=\frac{9}{5}=1\frac{4}{5}\end{array}$

**Question 2:**

Calculate the values of the following:

$\begin{array}{l}\text{(a)}\sqrt[3]{\frac{16}{250}}\\ \text{(b)}\sqrt[3]{-\frac{4}{256}}\\ \text{(c)}\sqrt[3]{0.008}\\ \text{(d)}\sqrt[3]{0.729}\end{array}$

Solution:Solution:

$\text{(b)}\sqrt[3]{-\frac{4}{256}}=\sqrt[3]{-\frac{1}{64}}=-\frac{1}{4}$

$\begin{array}{l}\text{(c)}\sqrt[3]{0.008}=\sqrt[3]{\frac{8}{1000}}\\ \text{=}\frac{2}{10}\\ \text{}=0.2\end{array}$

$\begin{array}{l}\text{(d)}\sqrt[3]{-0.729}=\sqrt[3]{-\frac{729}{1000}}\\ \text{}=-\frac{9}{10}\\ \text{}=-0.9\end{array}$

**Question 3:**

Find the value of
$\sqrt[3]{3\frac{3}{8}}+\sqrt{2\frac{14}{25}}.$

Solution:Solution:

**Question 4:**

Find the values of the following:

^{3}. (a) 1 – (–0.3)

${\left(2.1\xf7\sqrt[3]{27}\right)}^{2}$
(b)

Solution:Solution:

**(a)**

1 – (–0.3)

^{3 }= 1 – [(–0.3) × (–0.3) × (–0.3)] = 1 – (–0.027)

= 1 + 0.027

=

**1.027****(b)**

**Question 5:**

Find the values of the following:

$\begin{array}{l}\text{(a)}{\left(9+\sqrt[3]{-8}\right)}^{2}\\ \text{(b)}\sqrt{144}\xf7\sqrt[3]{216}\times {0.3}^{3}\end{array}$

Solution:Solution:

$\begin{array}{l}\text{(b)}\sqrt{144}\xf7\sqrt[3]{216}\times {0.3}^{3}\\ \text{}=144\xf76\times \left(0.3\times 0.3\times 0.3\right)\\ \text{}=24\times 0.027\\ \text{}=0.648\end{array}$