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TheLostOne
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Am I taking crazy pills? 22 Aug 2014, 14:58
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I was doing the mini quiz at the end of the exponents lessons and the question was:

√(12x32x54)

They simplified it to

2√3 x 4√2 x 3√6

Unless I am going insane, I don't see how 32 simplifies to 4√2. It is 2^5, so it would be 2√8

Please confirm sanity.

Thanks!
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mikemcgarry
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Am I taking crazy pills? 25 Aug 2014, 11:46
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TheLostOne
I was doing the mini quiz at the end of the exponents lessons and the question was:

√(12x32x54)

They simplified it to

2√3 x 4√2 x 3√6

Unless I am going insane, I don't see how 32 simplifies to 4√2. It is 2^5, so it would be 2√8

Please confirm sanity.

Thanks!
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Dear TheLostOne,
I'm happy to help. :-) I don't think you are losing your sanity, but 32 actually does simplify to 4√2.

First of all, see:
https://magoosh.com/gmat/2012/simplifyin ... -the-gmat/

You see, 32 = 4*8 but it also equals 32 = 2*16. Thus,
\(sqrt(32) = sqrt(16*2) = sqrt(16)*sqrt(2) = 4sqrt(2)\)

In fact, it's good to notice that \(sqrt(8)\) is not simplified, because 8 = 4*2; thus
\(sqrt(8) = sqrt(4*2) = sqrt(4)*sqrt(2) = 2sqrt(2)\)
The GMAT will never give you an answer in which \(sqrt(8)\) appears --- they will always expect you to simplify that.

Thus, even though it's true that the square root of 32 does equal \(2sqrt(8)\), that's not fully simplified.
\(sqrt(32) = 2sqrt(8) = 2*2sqrt(2) = 4sqrt(2)\)
Once again, the GMAT will always expect you to simplify fully each radical expression. If you partially simplify, your answer may be mathematically equal to what it should equal but not listed as a correct answer.

Does all this make sense?
Mike :-)