Problem 88 - Introductory Algebra for College Students

Question

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. When I use the square root property to determine the length of a right triangle's side, I don't even bother to list the negative square root.

Step-by-Step Solution

Answer

The statement makes sense because when finding the length of a right triangle's side using the square root property, only the positive root is considered, since lengths can't be negative.

Step 1: Understand the statement

The statement mentions that when using the square root property to determine the length of a right triangle's side, one does not list the negative square root. This triangulation method implies the Pythagorean theorem.

Step 2: The Square root property

When using the square root to solve equations or to find the magnitude of a quantity like the length of a side of a triangle, we consider both the positive and negative roots, because the square of both positive and negative numbers gives a positive result.

Step 3: Explanation of the theorem in the context of the statement

In the context of a right triangle, however, we only consider the positive root, because lengths (such as the sides of a triangle) cannot be negative.

Step 4: Final evaluation of the statement

Therefore, given the stated context of a right triangle, the statement that we do not consider the negative root when determining the length of a right triangle's side using the square root property makes complete sense.