# Why It Matters: Roots and Rational Exponents

## Why Learn About Roots and Rational Exponents?

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

Joan learns that [latex]c^2[/latex] represents the square of the length of the longest 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 does not 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.

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## Licenses & Attributions

### CC licensed content, Original

- Screenshot: Go To Sleep!.
**Provided by:**Lumen Learning**License:**CC BY: Attribution. - Why It Matters.
**Provided by:**Lumen Learning**License:**CC BY: Attribution.

### CC licensed content, Shared previously

- Cat Ladder.
**Authored by:**quaood's channel.**License:**All Rights Reserved.**License terms:**Standard YouTube License. - College Algebra.
**Provided by:**OpenStax**Authored by:**Abramson, Jay et al..**Located at:**https://cnx.org/contents/[email protected]:1/Preface.**License:**CC BY: Attribution.**License terms:**Download for free at: http://cnx.org/contents/[email protected]:1/Preface.