First Page Preview

First page of Adding Square Roots<subtitle>Situation 14 From the MACMTL-CPTM Situations Project</subtitle>

Mr. Fernandez was concerned about his ninth-grade algebra students’ responses to a recent quiz on radicals, specifically those in response to a question about square roots, in which students added

2
and
3
and obtained
5
as a result.

The mathematical basis for determining the appropriateness of the students’ work is that the sum of the square roots of two numbers is not, in general, equal to the square root of the sum of the two numbers. Establishing that a statement is not true can be accomplished in different ways, including finding a counterexample and constructing an indirect proof. The students’ statement,

2+3=5
⁠, can be disproved using numeric, geometric, and symbolic representations. Connections are also made to linear transformations.

Licensed reuse rights only
You do not currently have access to this chapter.
Don't already have an account? Register

Purchased this content as a guest? Enter your email address to restore access.

Please enter valid email address.
Email address must be 94 characters or fewer.