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anonymous
 5 years ago
sqrt (1/12)  sqrt (1/27)
anonymous
 5 years ago
sqrt (1/12)  sqrt (1/27)

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0When you have the sqrt of a fraction, it is the sqrt of the numerator divided by the sqrt of the denominator. Can you convert both expressions to a fraction with denominator 6?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes I can. The first thing you want to do is get the 1's out of the squareroot. \[\sqrt{a/b}=\sqrt{a}/\sqrt{b}\] So \[\sqrt{1/b}=\sqrt{1}/\sqrt{b}=1/\sqrt{b}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Does that make sense or did I use too many symbols and make it too long winded?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no it makes sense thank u!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The next thing to do is to simplify \(\sqrt{12},\sqrt{27}\)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do you know how to do that?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0find a common denominator?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Basically, what he's saying is that 1/sqrt(a) = sqrt(a) / a. This is because you can multiply by sqrt(a)/sqrt(a) and the root on the bottom cancels out, while the 1 on the top becomes sqrt(a). You get sqrt(12)/12  sqrt(27)/27, and you know how to simplify from there.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0That's probably a simpler way to look at it, I was going to simplify the denominator and then move it to the top.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But regardless, you need to simplify the radical.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but they dont reely have a common denominator do they?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0would it be 3 * 4 and 3 * 9 for it?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0In order to simplify a radical like \(\sqrt{12}\), you need to find a square that divides it. In this case, 4 divides 12, so we write \[\sqrt{12}=\sqrt{4}\sqrt{3}=2\sqrt{3}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Would you prefer to move everything to the top and then deal with it or deal with it first, then move it to the top?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0either way is easiest

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i mean whichever way is easiest

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Let's do it the way quantummodulus suggested. Did you understand what they said?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok. So what have you gotten to so far?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0(sqrt 12/2 sqrt 3)  (sqrt 27/3 sqrt 3)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok, not quite. I think we got you jumbled up a bit. Let's take a step back. First, we're going to do what is called rationalizing the denominator. That is where we multiply the top and the bottom by the denominator. This will get rid of the square root. Do you know how to do this?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok, so what do you get after rationalizing the denominator?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i think i square rooted something that didnt need to be sqaure rooted

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so now i have sq rt 12/12  sqrt 27/27 the denominators not being sqrt

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yup, perfect. Now, simplify the radical, like you did before.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay i got 2 sqrt 3/12  3 sqrt 3/27

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Right, now cancel and add fractions.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yup, now common denominators and add.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\(3*\sqrt{3}\) doesn't equal 3, same for the other fraction

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.03 sqrt 3/18  2sqrt 3/9

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sqrt 3/18 is the answer then?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yup. So the process is: rationalize the denominator, simplify the radical, simplify fractions

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Sorry about all of the confusion at the beginning.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh no that was my fault thank u for all your help thank u!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You're welcome. Good luck on any other problems.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\sqrt{a}\sqrt{b} = \sqrt{a2\sqrt{a*b}+b}\] Plug in 1/12 for a and 1/27 for b and simplify. The result is: \[{\sqrt{1\over 108}} = {1 \over 6\sqrt{3}}\] The formula is obtained by squaring the quantity radical a  radical b, ie: the left side of the formula equation. The first and last terms of the result is a and b respectively. The mid term is negative two times the product of radical a and radical b. Radical a times radical b is equal to the square root of the product of a and b. The final operation is to take the square root of every thing.
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