Question

A square rug has an area 99 ft2. Write the side length as a square root. Then decide if the side length is a rational number.

Answer 1

Hey there! I'm happy to help!

All of the sides of a square are the same. Therefore, to find the area, you multiply the side by itself. Multiplying a number by itself is conveniently called squaring.

Doing this backwards is called finding the square root. If you have an area of 64, you square root it, showing you that the sides are 8.

This means the side length of our square rug is √99.

A rational number is one that can be written as a fraction of two integers. If you put √99 into your calculator, you get 9.949874371....

This is not a rational number because it goes on forever in no particular order, so we cannot write it as a fraction of two integers. The closest number we could use to have a rational square root would be 100, as its square root is 10.

Have a wonderful day! :D