Question

PotteryPro needs to create a square label for the side of the box. In order to fit their graphic and instructions, the company would like the label to be 500cm2. How many centimeters will each side of the label measure?

Answer 1

The Area formula of the square is :

$A=s^2$

where s is the side of the square.

From the problem, the area of the square is A = 500 cm^2

Using the formula above :

$\begin{gathered} s^2=500 \\ \sqrt[]{s^2}=\sqrt[]{500} \\ s=\sqrt[]{500} \end{gathered}$

As you can see, we have s^2, and to get the value of s, we need to get the square root of both sides, so we will have s = √500

Next step is to factor 500 in which one factor is a perfect square.

Note that 500 = 100 x 5

and 100 is a perfect square.

So the equation will be :

$s=\sqrt[]{100\times5}$

we can extract the root of 100, which is 10.

√100 = 10

and the equation will become :

$\begin{gathered} s=\sqrt[]{100}\times\sqrt[]{5} \\ s=10\sqrt[]{5} \end{gathered}$

The answer is 10√5 cm