Find the side length of a square whose area is 45 square centimeters.
We know that the area of any shape is the space inside it. In this question, we have a square of area 45 square centimeters. We know that the area of any square is equal to 𝐿 squared, the side length squared. In this question, 𝐿 squared is therefore equal to 45. As square rooting is the opposite or inverse of squaring, we then need to square root both sides to calculate the value of 𝐿. 𝐿 is therefore equal to the square root of 45 or root 45.
We could type this into the calculator. However, in this case, to get an exact answer, we will simplify the radical or surd. We recall that our square numbers are one, four, nine, 16, 25, and so on. All these numbers can be square rooted to give a whole number or integer answer. To simplify any radical or surd, we look for a factor pair where one of the factors is a square number greater than one.
In this case, nine multiplied by five is 45. Therefore, root 45 can be written as root nine multiplied by root five. We know that the square root of nine is three as three squared equals nine. 𝐿 is therefore equal to three root five.
The side length of a square whose area is 45 square centimeters is three root five centimeters.