Problem 169 - College Algebra

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 does make sense because length represents distance, which isn't negative. When using the square root property to determine the length of a right triangle's side, it's not necessary to list the negative square root.

Step 1: Understand Square Root Property

The square root property states that if \(x^2 = k\), then \(x = \sqrt{k}\) or \(x = -\sqrt{k}\). Here, \(x\) can be either positive or negative. It's important to remember that a square root of a number always has two values: one positive and one negative.

Step 2: Apply Knowledge About Triangles

The lengths of the sides of a triangle are always nonnegative. This fact comes from the properties of a triangle. No side can have a negative length because length represents distance and distance isn't negative.

Step 3: Analyze The Statement

Given this information and knowing that the lengths of sides of a triangle are always nonnegative, the original statement makes sense. When using the square root property to determine the length of a right triangle's side, there would be no need to list the negative square root for this real-world physical quantity.