SOLUTION: I have been working on this math problem and I can't figure it out!! I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Properties o

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Question 176293This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been working on this math problem and I can't figure it out!! I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!!
Properties of Radicals
Simplify.
%284sqrt%283%29%29%2Fsqrt%2812%29
 This question is from textbook Algebra and Trigonometry Structure and Method book 2

Found 3 solutions by Alan3354, EMStelley, Edwin McCravy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
4 square root of 3 over the square root of 12.
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I think you mean 4th root of 3 over sqrt of 12, not "4th square root
3%5E%281%2F4%29%2Fsqrt%2812%29
=3%5E%281%2F4%29%2F12%5E%281%2F2%29
=3%5E%281%2F4%29%2F%282%2A%283%5E%281%2F2%29%29%29
=3%5E%283%2F4%29%2F%282%2A%283%29%29
= (4th root of 27)/6
It's a bit confusing. If you can't follow it, email me.

Answer by EMStelley(208) About Me  (Show Source):
You can put this solution on YOUR website!
Just to clarify, the problem is:
4sqrt%283%29%2Fsqrt%2812%29
Note that sqrt(3) is as simplified as its going to get, so let's concern ourselves with sqrt(12). Now, 12 can be written as 4*3, so that means that
sqrt%2812%29=sqrt%284%2A3%29
The properties of square roots tell us that sqrt(ab)=sqrt(a)sqrt(b), so
sqrt%2812%29=sqrt%284%2A3%29=sqrt%284%29sqrt%283%29
But sqrt(4)=2, so we can replace that, and thus we have
4sqrt%283%29%2Fsqrt%2812%29=4sqrt%283%29%2F%282sqrt%283%29%29
Now, 4/2=2, and the sqrt(3)'s cancel out, so all we are left with is 2!!

Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!

%284sqrt%283%29%29%2Fsqrt%2812%29

Write the 12 as 4%2A3

%284sqrt%283%29%29%2Fsqrt%284%2A3%29

Take individual square roots on the bottom:

%284sqrt%283%29%29%2F%28sqrt%284%29sqrt%283%29%29

Replace sqrt%284%29 on the bottom by 2:

%284sqrt%283%29%29%2F%282sqrt%283%29%29

Cancel the sqrt%283%29's

%284cross%28sqrt%283%29%29%29%2F%282cross%28sqrt%283%29%29%29

4%2F2

2

Edwin