**2.1 Squares, Square Roots, Cube and Cube Roots**

**(A) Squares**

The square of a number is the answer you get when
you multiply a number by itself.

**Example 1:**

(a) 13^{2}
= 13 × 13 = **169**

(b) (–10)^{2}
= (–10) × (–10) = **100**

(c) (0.4)^{
2} = 0.4 × 0.4 = **0.16**

(d) (–0.06)^{2}
= (–0.06) × (–0.06) = **0.0036**

$\begin{array}{l}\text{(e)}{\left(3\frac{1}{2}\right)}^{2}={\left(\frac{7}{2}\right)}^{2}=\frac{7}{2}\times \frac{7}{2}=\frac{49}{4}\\ \left(\text{f}\right)\text{}{\left(-1\frac{2}{7}\right)}^{2}={\left(-\frac{9}{7}\right)}^{2}=\left(-\frac{9}{7}\right)\times \left(-\frac{9}{7}\right)=\frac{81}{49}\end{array}$
**(B) Perfect Squares**

**1.**
**Perfect
squares** are the **squares of whole numbers**.

**2.**
**Perfect squares** are formed by **multiplying a whole number by itself**.

**Example:**

4 = 2 × 2 9
= 3 × 3 16 = 4 × 4

**3.**
The first twelve perfect squares are:

= 1^{2}, 2^{2}, 3^{2}, 4^{2},
5^{2}, 6^{2}, 7^{2}, 8^{2}, 9^{2}, 10^{2},
11^{2}, 12^{2}

**=
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144**

**(C) Square Roots**

1. The square root of a positive number is a number
multiplied by itself whose product is equal to the given number.

**Example 2:**

$\begin{array}{l}\text{(a)}\sqrt{169}=\sqrt{13\times 13}=13\\ \text{(b)}\sqrt{\frac{25}{64}}=\sqrt{\frac{5\times 5}{8\times 8}}=\frac{5}{8}\\ \text{(c)}\sqrt{\frac{72}{98}}=\sqrt{\frac{\overline{)72}36}{\overline{)98}49}}=\sqrt{\frac{6\times 6}{7\times 7}}=\frac{6}{7}\\ \text{(d)}\sqrt{3\frac{1}{16}}=\sqrt{\frac{49}{16}}=\frac{7}{4}=1\frac{3}{4}\\ \text{(e)}\sqrt{1.44}=\sqrt{1\frac{\overline{)44}11}{\overline{)100}25}}=\sqrt{\frac{36}{25}}=\frac{6}{5}=1\frac{1}{5}\end{array}$