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As you've come to realize, you have to be careful when factoring out numbers from large calculations.

There are actually several different ways to 'factor down' and simplify this question, but your second approach is correct (and is just as valid as any other).

Here's another way to do it (based on the same ideas that you were using):

You might catch that 16 is a factor of BOTH terms (16x20 and 8x32). By factoring out 16, we can simplify the calculation even further....

Check highlighted portion, when u took out 2^3 , outside the root, basically you left inside only 2^2. However in highlighted portion, you marked it as 2^4 and hence the wrong answer.
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You CAN factor out a 4, but I'd like to see your work so that we can assess whether you're factoring out that 4 correctly or not. So, can you post your work/"steps"?

As an aside, after factoring out a 4, you'd then have more work to do to get to the solution.

4[(4*5)+(2*8)] 4[20+16] 4[36] take the square root... (2)(6)=12

However, I now realize that the way I was factoring it, I actually was taking out 'too many' 4's and I should have done it like so...is this right? 4[(16*5)+(8*8)] 4[80+64] 4[144] take the square root... 2*12=24

why is 16 only factored from 2 and the 20 and 8 are left alone? sorry if this is a bad question, I'm new to the gmat and need every explanation i could get

why is 16 only factored from 2 and the 20 and 8 are left alone? sorry if this is a bad question, I'm new to the gmat and need every explanation i could get

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