A Trip through History (Multiplying, Dividing, and Rationalizing Square Roots)
Description of student activity:
Students will learn and practice the product and quotient properties of square roots as well as rationalizing monomial and binomial denominators. They will do this while also learning why rationalization is useful today as well as practice why it was useful prior to square rooting calculators.
To start this activity, students (or the teacher) will read the introductory handout pages. This handout will explain the product and quotient properties of square roots, rationalizing monomial denominators, and rationalizing binomial denominators with the conjugate.
After completing the handout, students will be guided through an explanation of why rationalizing is used now as well as why it was useful prior to calculators with a square root function. They will then practice simplifying radial expressions using a table of square root values instead of the square root function on their calculators. The resulting numbers will be multiplied together on their calculator and they will pretend they have an extended “Multiplication Table”.
The next section explains why rationalizing the denominator made simplifying fractions much easier by using a long division example of a rationalized and non-rationalized denominator in combination with the square root table. Students will then practice rationalizing monomial denominators and rationalizing binomial denominators with a conjugate.
Lastly, students will complete 7 matching problems while able to use their calculators fully. Some of these problems include variables that require rationalizing instead of simply using their calculators.
- Lesson Handout (2 pages)
- Lesson (4 pages)
- Answer Key (4 pages)
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