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Dividing Radicals: 45-45-90 Triangle

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by Brent@GMATPrepNow » Fri Mar 07, 2014 1:45 pm
JScherman wrote:Image

Can anyone explain how the 4/√2 is simplified to 2√2
Mathematically speaking, it's considered "bad form" to have a radical (root) in the denominator of a fraction.
To fix this, we need to create an EQUIVALENT fraction that doesn't have this problem.

So, take 4/√2 and multiply top and bottom by √2 to get: [4√2]/[(√2)(√2)]
Evaluate: [4√2]/2
Simplify: 2√2

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Brent
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by Matt@VeritasPrep » Sat Mar 08, 2014 10:15 am
You can also break up 4. Since you know you want to get rid of a √2, try finding √2 inside 4, like this:

4
--
√2

is really

2 * 2
-----
√2

is really

√2 * √2 * 2
-----------
√2

is really

2√2

I usually do it this way in my head - tends to be quicker.
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