Then, we went over today's lesson: Radical notation for Nth roots. We finished with enough time to complete our homework assignment (so there is no homework tonight except read this blog- which- probably no one will do:)
Now I will get to the point, and summarize the lesson. Today's point was to link the idea of a number raised to a fraction (25^1/2) to the idea of a number under a radical(√25). This involved reviewing the notation from chapter 7.
x^1/2 meant the positive square root of x.
x^1/n meant the positive nth root of x.
So then we were able to justify this: ^n √ x= x^1/n. Conditions: x must be a positive integer and n must be an integer greater than 2.
So here is an example which will probably make more sense then the above.
^3 √512... THINK: ?^3=512... ANSWER: 8
After this we did a little more complicated problems but we just had to apply our knowledge of properties we learned back in chapter 7.
After practicing this, we came to the Root of a Power Theorem:
^n √x^m = X^m/n. Conditions: x must be a positive integer, n must be an integer greater than 2 and m must be an integer. After understanding this we applied it in this problem: ^3 √X^12... THINK: (X^12)^1/3... ANSWER: X^4
After this, we went to the geometric mean. This was a very easy concept. If we have data with n values, we multiply all of the numbers then take the ^n square root of that product. I will not waste space by giving a lengthy example so I will make it super easy: data is : 1,3,4,6... product is 72. then take the 4th root of 72. Answer is 8. 48.. easy right? :)
Then came the concept of roots of roots. √√x hmm... all you do here is however many radical signs there are, you just multiply them. In this case there are 3. So that's like doing 1/2*1/2*1/2 which is 1/8. so x^1/8. But now is the A-HA moment where we can use what we learned today. We now can call X^1/8 the ^8√x
example: √L^4...THINK: (L^4)^1/2... So 4/2=2... L^2.
So that is the lesson in a nutshell! The notes are very meaty and helpful if the above summarization didn't work for you. Also, Mr. Cope stressed that his door is wide open if anyone is struggling.