Math geniuses only?

Question

simplify the following- square root symbol (long check thing) aka radical sign over (6+3 sqroot 3 minus (-) square root symbol over 6-3 sqroot 3 ) ^2 (everything in parentheses to an exponent of 2) any answers or clue of what im talking about , it would be so much simpler with a square root symbol

Answer 1

You might hate the rigged problem after this, but treat it as a normal FOIL problem (the first nasty sqrt as x and the second as y)

So:
sqrt(6+3sqrt(3)) = x
sqrt(6-3sqrt(3)) = y

(x-y)^2 = x^2 - 2xy + y^2

Well x^2 and y^2 is easy just take away the big sqrt:

(6+3sqrt(3)) - 2xy + (6-3sqrt(3))

Now for the middle term, just multiply the stuff under the radicals, (another FOIL problem):

sqrt( (6+3sqrt3)*(6-3sqrt3) ) = sqrt(36 - 27) = sqrt9 = 3

So now you have:

(6+3sqrt3) + 2(3) + (6-3sqrt3)

Do a little canceling:

6 - 6 + 6 = 6

Deceptively hard.

Answer 2

Assuming that the (6+3√3) and (6-3√3) are in parenthesis I understand this to be your equation:

√([(6+3√3)-(6-3√3)]²)

If this is the case...

The radical and the exponent cancel each other out, therefore we are left with this:

[(6+3√3)-(6-3√3)]

How to solve:

1) Distribute the negative from -(6-3√3) inside the parenthesis
2) Now we have [6+3√3+-6+3√3]
3) The 6's cancel out leaving us with 3√3 + 3√3
4) 3√3 + 3√3 = 6√3

By the way, to insert the radical sign go to Start > Run and type in "charmap" without the quotes. Maybe this will make it easier to ask your question if I didn't interpret it correctly.

Answer 3

If your question is...
√((6 + 3√(3) - √(6) - 3√(3))^2)
Here is how you would solve it...

Notice that inside the problem has a square inside the square root. These two cancel each other out to make...
6 + 3√(3) - √(6) - 3√(3)
Now notice that there are two 3√(3)'s in the problem. There is a positive one and a negative one, so they cancel out to make...
6 - √(6)
This is the simpliest it can go!

Hope I helped!
10 points best answer?

Answer 4

[√(6 + 3√3) - √(6 - 3√3)]^2 =
6 + 3√3 -2√[36 - 18√3 + 18√3 - 27] + 6 - 3√3 =
6 -2√[36 - 27] + 6 =
6 -2√[9] + 6 =
6 - 6 + 6 =
6

Answer 5

I guess you pretty much mean

( Sqrt [ 6 +3Sqrt[3] ] - Sqrt [ 6 - 3Sqrt[3] ] )^2

where Sqrt = squareroot

Using (a-b)^2 = a^2 +b^2 - 2ab

So we have [ 6 + 3Sqrt[3] ] + [ 6 - 3Sqrt[3] ] - 2Sqrt[ 36 - 9x3 ]
= 12 - 2Sqrt[9]
= 12 - 6 = 6

Answer 6

(root(6+3root3 - root(6-3root3)^2
or 6+3root3 +6-3root3 - 2(root(6+3root3)*(root(6-3root3)
or 12-2(root(36-27)
or 12-2(root9)
or 12-2(3)
or 12-6
or 6 Ans

Answer 7

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Answer 8

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