Question

The area of a square plot of land is 325 square meters. What is the perimeter of the square, in meters? Express your answer in simplest radical form.

Answer 1

Hey there! I'm happy to help!

The first thing to do is find the square root of the area so we know what one of the sides are. Since our answer is supposed to have a radical, we don't need to simplify the radical.

So, each side is just √325.

Now, we multiply this by four to find the perimeter.

4√325

However, we can simplify that. To do this, we will find all of the prime factors of 325. If there are two of a certain number, we will take that number and pull it to the outside of the radical and cancel out both of the numbers inside the radical. So, if you had two 2's inside the radical, you would cancel them out and put a single two on the outside.

4√5×5×13

We can put the five outside

4×5√13

The perimeter is 20√13.

I hope that this helps! Have a wonderful day!