Simplest radical form
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Simplest radical form

[From: ] [author: ] [Date: 11-05-06] [Hit: ]
you can remove them from inside the radical and write their square root outside the radical instead.So, for √75, you know that 25 is a perfect square.But √(25 * 3) is the same as √25 * √3.And √25 is just 5,......
it says "Simplify each radical expression"
One of the problems is √75 , how do i get the answer? (show me steps please~)
Also on the other side it says "Perform the indicated operations. Write your answers in SRF"
One of the problems is 1/3√63
How do i do this?
THANK YOU !

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It means if there are any perfect squares inside the radical, you can remove them from inside the radical and write their square root outside the radical instead. Remember the following identities:

√(a * b) = √a * √b
√(a / b) = √a / √b

So, for √75, you know that 25 is a perfect square. So rewrite √75 as:
√75 = √(25 * 3)
But √(25 * 3) is the same as √25 * √3.
And √25 is just 5, so this is really 5√3.

Answer: √75 = 5√3.

Do the other problem pretty much the same way:
(1/3) √63 = (1/3) √(9 * 7)
(1/3) √(9 * 7) = (1/3) * √9 * √7.
(1/3) * 3 * √7.
But (1/3) * 3 is just 1, so the final answer is √7.

Answer: (1/3) √63 = √7

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sqr(75)=sqr(3*25) =sqr(3)*sqr(25) =5*sqr(3)
1/3*sqr(63)=1/3*sqr(3*9) =1/3*sqr(3)*3 =sqr(3)
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keywords: radical,Simplest,form,Simplest radical form
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