Why It Matters: Roots and Rational Exponents

Why learn about roots and rational exponents?

Go to sleep!

[latex]{a}^{2}+{b}^{2}={c}^{2}[/latex]

Joan learns that [latex]c^2[/latex] represents the long side of the right triangle, so in her case this is the length of ladder that she will need. She gets to work trying to solve the equation:

[latex]\begin{array}{ccc}\hfill {a}^{2}+{b}^{2}& =& {c}^{2}\hfill \\ \hfill {5}^{2}+{12}^{2}& =& {c}^{2}\hfill \\ \hfill 169& =& {c}^{2}\hfill \end{array}[/latex]

Joan gets this far and realizes she does not understand how to solve this kind of equation. She needs to find out the length that, when squared, is [latex]169[/latex], to determine which ladder to choose.

What she doesn't realize is that she needs to find a square root.

In this module, we will investigate methods of finding solutions to problems such as this one.  We will revisit Joan later and see if she and Jacob were successful in making a cat ladder for Hobbes.

Learning Outcomes:

• Define, evaluate, and simplify roots
• Simplify radical expressions using algebraic operations
• Rationalize denominators
• Solve radical equations
• Solve applications of radical equations

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