The square root of 3000 can be approximated by comparing it to two nearby perfect squares that are less than 3000 and greater than 3000.
≈ 55 feet
Practice makes perfect
We have a square helicopter launching pad with an area of 3000ft^2. Recall 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 3000 is not a perfect square and we are not asked for an exact answer, we can find an approximation by comparing 3000 to the nearest two perfect squares. We will use a perfect square less than and a perfect square greater than 3000. Let's try 2916 and 3025.
Now we know that the side length must be some number between 54 and 55. To decide which value is our answer, we need to determine to what number 3000 is closer to — 2916 or 3025.
2916<30_(84)00<3025_(25)
The difference between 2916 and 3000 is 84, while the difference between 3000 and 3025 is 25. Therefore, 3000 is closer to 3025 and, subsequently, sqrt(3000) is closer to sqrt(3025). We conclude that the side length of the helicopter pad is approximately 55 feet.
