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Study Guides > College Algebra CoRequisite Course

Introduction to Radicals and Rational Exponents

Learning Outcomes

By the end of this section, you will be able to:
  • Evaluate square roots.
  • Use the product rule to simplify square roots.
  • Use the quotient rule to simplify square roots.
  • Add and subtract square roots.
  • Rationalize denominators.
  • Use rational roots.
A hardware store sells 16-ft ladders and 24-ft ladders. A window is located 12 feet above the ground. A ladder needs to be purchased that will reach the window from a point on the ground 5 feet from the building. To find out the length of ladder needed, we can draw a right triangle as shown in Figure 1, and use the Pythagorean Theorem.
A right triangle with a base of 5 feet, a height of 12 feet, and a hypotenuse labeled c Figure 1

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

Now we need to find out the length that, when squared, is 169, to determine which ladder to choose. In other word we need to find a square root. In this section we will investigate methods of finding solutions to problems such as this one.

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  • College Algebra. Provided by: OpenStax Authored by: Abramson, Jay et al.. License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].

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