Conclusion
At the beginning of this lesson, we left Joan and her sister as they were planning to make a ramp for Joan's cat Hobbes from her window. She used the Pythagorean Theorem to get this far, but was left with an equation she didn't know how to solve:
[latex-display]\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-display]
The goal was to find the unknown length in the following triangle, where c represents the length of the cat ladder.
Joan's sister, Anne, suggested that she use a square root to find the solution to her equation. Joan remembered that roots and exponents are related - one "undoes" the other. She tried it out in the following way:
[latex-display]\begin{array}{ccc}169 ={c}^{2}\\\sqrt{169}=\sqrt{c^2}\\13=c\end{array}[/latex-display]
Hooray! Joan has the length she needs to create her cat's ladder. Hopefully she will be able to get some sleep now.
