Question

sqrt (1/12) - sqrt (1/27)

Answer 1

When 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?

Answer 2

Yes 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 \[\sqrt{1/b}=\sqrt{1}/\sqrt{b}=1/\sqrt{b}\]

Answer 3

o okay

Answer 4

Does that make sense or did I use too many symbols and make it too long winded?

Answer 5

no it makes sense thank u!

Answer 6

The next thing to do is to simplify \(\sqrt{12},\sqrt{27}\)

Answer 7

do you know how to do that?

Answer 8

find a common denominator?

Answer 9

Basically, 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.

Answer 10

That's probably a simpler way to look at it, I was going to simplify the denominator and then move it to the top.

Answer 11

But regardless, you need to simplify the radical.

Answer 12

but they dont reely have a common denominator do they?

Answer 13

would it be 3 * 4 and 3 * 9 for it?

Answer 14

In 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
\[\sqrt{12}=\sqrt{4}\sqrt{3}=2\sqrt{3}\]

Answer 15

Right, exactly.

Answer 16

Would you prefer to move everything to the top and then deal with it or deal with it first, then move it to the top?

Answer 17

either way is easiest

Answer 18

i mean whichever way is easiest

Answer 19

Let's do it the way quantummodulus suggested. Did you understand what they said?

Answer 20

yes

Answer 21

Ok. So what have you gotten to so far?

Answer 22

(sqrt 12/2 sqrt 3) - (sqrt 27/3 sqrt 3)

Answer 23

Ok, 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?

Answer 24

yes

Answer 25

Ok, so what do you get after rationalizing the denominator?

Answer 26

i think i square rooted something that didnt need to be sqaure rooted

Answer 27

so now i have sq rt 12/12 - sqrt 27/27 the denominators not being sqrt

Answer 28

Yup, perfect. Now, simplify the radical, like you did before.

Answer 29

on top?

Answer 30

Yup.

Answer 31

okay i got 2 sqrt 3/12 - 3 sqrt 3/27

Answer 32

Right, now cancel and add fractions.

Answer 33

sqrt 3/6 - sqrt3/9

Answer 34

Yup, now common denominators and add.

Answer 35

3/18 - sqrt 6/18

Answer 36

\(3*\sqrt{3}\) doesn't equal 3, same for the other fraction

Answer 37

3 sqrt 3/18 - 2sqrt 3/9

Answer 38

/18

Answer 39

now just subtract

Answer 40

sqrt 3/18 is the answer then?

Answer 41

Yup. So the process is: rationalize the denominator, simplify the radical, simplify fractions

Answer 42

Sorry about all of the confusion at the beginning.

Answer 43

oh no that was my fault thank u for all your help thank u!

Answer 44

You're welcome. Good luck on any other problems.

Answer 45

\[\sqrt{a}-\sqrt{b} = \sqrt{a-2\sqrt{a*b}+b}\]
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.