Video Transcript
A squared mosaic is made up of 1,800 white squares and 1,800 black squares of equal sizes. Determine the number of squares required to make one side of the mosaic.
In this question, we are told that a square mosaic is made up of 1,800 white squares and 1,800 black squares of the same size. We need to determine how many squares make up one side of the mosaic. To find this value, let’s start by sketching a picture of the square mosaic.
We can say that there are 𝑛 squares that make up each side of the mosaic. We can then note that 𝑛 must be a whole number of squares. The mosaic itself is made up of 1,800 white squares and 1,800 black squares. So we can add these together to find the total number of squares. This gives us that the mosaic is made up of 3,600 squares. We can then note that the square is made up of 𝑛 squares by 𝑛 squares of the same size. So, the total number of squares must be 𝑛 times 𝑛, which is 𝑛 squared. Hence, 𝑛 squared is equal to 3,600.
There are a few different ways of finding the value of 𝑛. One way is to note that 3,600 is equal to 60 times 60, so it is 60 squared. We can then recall that if 𝑎 is positive, then the square root of 𝑎 squared is equal to 𝑎. So we can take square roots of both sides of the equation, where we note that 𝑛 is positive, to get that 𝑛 is equal to 60.
We can check our answer by considering how many squares would be in a mosaic made up of a grid of 60 congruent squares by 60 congruent squares. We can then calculate that there would be 60 times 60 squares, which is equal to 3,600 squares in the mosaic. This is the same as the question, so it confirms our answer that one side of the mosaic will be made up of 60 squares.
