We are given square roots that we cannot calculate without a calculator. However, we can estimate their values using nearby perfect squares. First we will estimate the roots and then we can determine whether a triangle with the given side lengths is possible.
Estimating the Roots
Let's begin by considering the first given value, sqrt(99). We want to look for the perfect squares nearest to 99. Then we can compare their square roots in a compound inequality.
sqrt(81)
Since 99 is closer to 100, the square root of 99 is closer to the square root of 100. Therefore, we can say that sqrt(99) is approximately 10.
sqrt(99)≈ 10
We can follow the same line of thinking for the other two roots.
