Exercises: Square Roots

In the following table the side length $a$ of a square or its area $A_{□}$ is given.

Some values are still missing in the tables. Calculate them without a pocket calculator.

a	$4 cm$	?	$1 m$	$7 cm$
$A_{□}$	?	$49 m^{2}$	?	?

a	?	$10 mm$	?	?
$A_{□}$	$81 {cm}^{2}$	?	$121 {dm}^{2}$	$25 {cm}^{2}$

In this exercise, for example, you can first calculate the missing area values and then the missing side lengths.

Calculating the areas

You can determine the area of a square usingthe formula:

A_{□} = a^{2} = a \cdot a

Now use the formula to calculate the missing area values:

$a = 4 cm \Rightarrow A_{□} = (4 cm)^{2} = 16 {cm}^{2}$

$a = 1 m \Rightarrow A_{□} = (1 m)^{2} = 1 m^{2}$

$a = 7 cm \Rightarrow A_{□} = (7 cm)^{2} = 49 {cm}^{2}$

$a = 10 mm \Rightarrow A_{□} = (10 mm)^{2} = 100 {mm}^{2}$

Calculating of the side lengths

To get the missing side lengths, you need to find out, which number, when multiplied by itself, becomes the corresponding area.

So, for example, "Which number times, if multiplied by itself, becomes $49$ ?" $\to$ $7 \cdot 7 = 49$ , so the side length you are looking for is $7 m$ .

$\begin{array}{l} A_{□} = 49 m^{2} \Rightarrow 7 \cdot 7 = 49 \\ \Rightarrow a = 7 m \end{array}$

$\begin{array}{l} A_{□} = 81 {cm}^{2} \Rightarrow 9 \cdot 9 = 81 \\ \Rightarrow a = 9 cm \end{array}$

$\begin{array}{l} A_{□} = 121 {dm}^{2} \Rightarrow 11 \cdot 11 = 121 \\ \Rightarrow a = 11 dm \end{array}$

$\begin{array}{l} A_{□} = 25 {cm}^{2} \Rightarrow 5 \cdot 5 = 25 \\ \Rightarrow a = 5 cm \end{array}$

Solution


$a$	$4 cm$	$7 m$	$1 m$	$7 cm$
$A_{□}$	$16 {cm}^{2}$	$49 m^{2}$	$1 m^{2}$	$49 {cm}^{2}$


$a$	$9 cm$	$10 mm$	$11 dm$	$5 cm$
$A_{□}$	$81 {cm}^{2}$	$100 {mm}^{2}$	$121 {dm}^{2}$	$25 {cm}^{2}$

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