At the beginning of this lesson, we left Joan and her brother who 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:
a2+b252+122169===c2c2c2
The goal was to find the unknown length in the following triangle, where c represents the length of the cat ladder.
Joan's brother, Jacob, 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:
169=c2169=c213=c
Hooray! Joan has the length she needs to create her cat's ladder. Hopefully she will be able to get some sleep now.