Exercise 34 Page 450

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(8). We want to look for the perfect squares nearest to 8. Then we can compare their square roots in a compound inequality. sqrt(4)Since 8 is closer to 9, the square root of 8 is closer to the square root of 9. Therefore, we can say that sqrt(8) is approximately 3. sqrt(8)≈ 3 We can follow the same line of thinking for the other two roots.

Can It Be a Triangle?

Now, using our approximated values we can use the Triangle Inequality Theorem.

Let's verify if this theorem is true for these three roots. If yes, then it is possible to form a triangle with the given side lengths.

The first case does not satisfy the theorem. Therefore, the given side length cannot be used to form a triangle.