8-6 Quotients with Radicals

When we came into class on Wednesday, Mr. Cope had watched the video he recorded from the day before. After watching the video, he said he noticed two things: he answers his own questions sometimes, and that if you don't want to participate in class, then this class is fairly easy because you can just sit back and listen. He decided to take a new approach for the day to get everyone involved by using small erase boards and doing problems on them.

In today's lesson we learned about rationalizing the denominator. It is very similar to imaginary numbers if you look back to chapter six. It is the same concept, getting the radical out of the denominator. We started with easier examples:

3
--
√4 from here, you need to multiply the fraction by a WFOO (weird form of one)

3 √4 3 √4 3√4
--- x ---- = ----- = ----
√4 √4 √16 4


For the next examples, you need to multiply the numerator and the denominator by the conjugate, for example:

2 3 - √6 6 - 2√6
---- x -------- = --------
3 + √6 3- √6 3


Some of the harder examples, ones that you need to use information from both 8.5 and 8.6, look like this:

y^2 y^2
---- first, you need to simplify the denominator ------
√y^7 y^3√y


then, you need to get the radical out of the denominator
y^2 √y y ^2√y √y
--------- x ---- = ---------- = -------
y^3 √y √y y^4 y^2

We’re having a quiz on this section along with 8.4 and 8.5 tomorrow so hopefully this helps out!