[RESOLVED] Square roots

How do you simplify the equation not by using a calculator:

Sqrt 192 ?

Its not a perfect square so I remember there is a formula but its been so long since I have done it that I forget :(

Thanks

Simplify as in Sqrt(192) = 8 * Sqrt(3)?

Sqrt(192) = Sqrt(64 * 3) = Sqrt(64) * Sqrt(3) = 8 * Sqrt(3)

Yes, but thats like trial an error. Isnt there some standard formula for it?

(8) * Sqrt(3)

But how to get to that point?

Quote:

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Originally Posted by RobDog888

Yes, but thats like trial an error. Isnt there some standard formula for it?

(8) * Sqrt(3)

But how to get to that point?

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Naw you gotta find the factors of 192 and see if any of them is a square. Its brute force I can't think of any other way.

So there would be that one answer only?
You wouldnt break 8 down into 2*2*2?

Quote:

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Originally Posted by RobDog888

So there would be that one answer only?
You wouldnt break 8 down into 2*2*2?

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Right I think the goal is to get as much of the number outside of the square root.

Ok, so ...

(2)*(2)*(2)*sqrt(3) should be the answer.

I cant believe i forgot so much math. I used to know calculus and physics. :(

Actually, it stems from this:
Sqrt(192) = Sqrt(2^6 * 3)
Separate even powers from odd:
= Sqrt(2^6) * Sqrt(3)
= 2^3 * Sqrt(3)
= 8 * Sqrt(3)

If you have something like Sqrt(2^3):
= Sqrt(2^2 * 2)
= Sqrt(2^2) * Sqrt(2)
= 2 * Sqrt(2)

Damn forgot its a negative...

-sqrt of 192

So would that be .... 8 * sqrt(3) or a negative sign in front of 8?

-Sqrt(192)
= -1 * Sqrt(192)
= -1 * 8 * Sqrt(3)
= -8 * Sqrt(3)

That seems to work.

Thanks guys.