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Chapter 0: Problem 64

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.

Short Answer

Expert verified
The statement makes sense as the length of a triangle's side, being a distance, cannot be negative; hence, only the positive square root is valid when using the square root property to determine this length.

Step by step solution

01

Understanding of square root property

Firstly, it's essential to recall what the square root property is. It states that if \(x^2 = a\), where a is a positive number and \(x\) is a variable, then \(x = \sqrt{a}\) or \(x = -\sqrt{a}\). This means any square number has two roots: positive and negative.
02

Understanding the concept of length in Geometry

Length in geometry is always a non-negative quantity. It's a measurement that cannot be negative as it represents distance between two points.
03

Applying understanding to the problem

In the context of the problem, when determining the length of a right triangle's side using the square root property, only the positive square root is considered valid. This is because lengths cannot be negative. Therefore, the statement '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' makes sense.

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