The Area formula of the square is :

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}](https://img.qammunity.org/2023/formulas/mathematics/college/tvcqrfhu936x61dyybmm3yn3ull35zo8a0.png)
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*5}](https://img.qammunity.org/2023/formulas/mathematics/college/axfv8pn8e0svj1ar48wgs5yxs68rsf5eth.png)
we can extract the root of 100, which is 10.
√100 = 10
and the equation will become :
![\begin{gathered} s=\sqrt[]{100}*\sqrt[]{5} \\ s=10\sqrt[]{5} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/qhsg53ovkd4rayi70ehocuuuwb0jgjpzcx.png)
The answer is 10√5 cm