The square root of 160 can be approximated by comparing it to two nearby perfect squares that are less than 160 and greater than 160.
≈ 13 in
Practice makes perfect
We have a square game board with an area of 160in^2 and are asked to approximate the side length to the nearest whole number. First, we need to remember that the area of a square is found by squaring the side length s.
A=s^2
By substituting the area into the formula we can find the side length. Notice that a length cannot be negative, so we only consider positive solutions.
Since 160 is not a perfect square and we are not asked for an exact answer, we can find an approximation by comparing 160 to the nearest two perfect squares. We will use a perfect square less than and a perfect square greater than 160. Let's try 144 and 169.
Now we know that the side length must be some number between 12 and 13. To decide which value is our answer, we need to determine to what number 160 is closer to — 144 or 169.
144<16_(16)0<169_9
The difference between 144 and 160 is 16 while the difference between 160 and 169 is 9. Therefore, 160 is closer to 169 and, subsequently, sqrt(160) is closer to sqrt(169). We conclude that the side length of the game board is approximately 13 in.
