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Source: — Problem Solving |

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by Brent@GMATPrepNow » Sat Jul 26, 2014 6:00 pm
tpz wrote:I keep getting 4 sq.root 20 + 16 every time I solve this problem.... but the answer is 24. please help.

sq root. of: (16)(20) + (8)(32)
the sq root sign is over the entire equation above.

thank you!
Useful mental math fact: AB = (A/2)(2B)
For example, (8)(15) = (4)(30)
In this example, we see that 16 is a perfect square (which is useful in square root questions), so we can factor it out of (16)(20).
Also, using our nice mental math rule, we can rewrite (8)(32) as (16)(16)


So, here we go....
sqrt[(16)(20) + (8)(32)] = sqrt[(16)(20) + (16)(16)]
= sqrt[16(20 + 16)]
= sqrt[16(36)]
= [sqrt16] [sqrt36]
= (4)(6)
= 24

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by [email protected] » Sat Jul 26, 2014 6:28 pm
Hi tpz,

When it comes to simplifying/solving these types of radicals, you are NOT allowed to "split" the calculation in the way that you did.

Here, you have a straight-forward enough calculation:

16(20) + 8(32)

320 + 256

576

From here, you can either take the square root of 576 OR use the answer choices and square them all to "work back up" to 576.

Either way, you'll get 24

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by GMATinsight » Sat Jul 26, 2014 9:17 pm
tpz wrote:I keep getting 4 sq.root 20 + 16 every time I solve this problem.... but the answer is 24. please help.

sq root. of: (16)(20) + (8)(32)
the sq root sign is over the entire equation above.

thank you!
Hi tpz,

You are getting absolutely correct result4 sq.root 20 + 16 and you need to solve it just one step forward. I am showing you the next step here

4 sq.root 20 + 16
I hope you mean, 4 sq.root (20 + 16)
i.e. 4 (sq.root 36)
i.e. 4 x 6 = 24 YOUR ANSWER :)
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by GMATGuruNY » Sun Jul 27, 2014 2:25 am
tpz wrote:√ ((16)(20)+ (8)(32)) =

(A) 4 sqrt(20)
(B) 24
(C) 25
(D) 4 sqrt(20) + 8 sqrt(2)
(E) 32
Try to factor out a PERFECT SQUARE.

√ (16*20 + 8*32)

= √ 4 (4*20 + 2*32)

= √ 4*144

= √4 * √144

= 2*12

= 24.

The correct answer is B.
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