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# root(16*20+8*32)=

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Intern
Joined: 23 Apr 2012
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23 Apr 2012, 09:35
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Difficulty:

5% (low)

Question Stats:

84% (01:52) correct 16% (01:37) wrong based on 157 sessions

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$$\sqrt{16*20+8*32}=$$

A. $$4\sqrt{20}$$

B. $$24$$

C. $$25$$

D. $$4\sqrt{20}+8\sqrt{2}$$

E. $$32$$

This question really should not be difficult, but the explanation given by GMAC seems to violate the rules of operations PEMDAS. sqrt((16)(20)+(16)(16)) simplified to... sqrt((16)(20+16)) I understand eliminating one of the 16s on the right since its essentially 16 squared, but I dont understand why they can then add 20 and 16 BEFORE multiplying by the left-hand 16
[Reveal] Spoiler: OA

Last edited by Bunuel on 23 Apr 2012, 10:28, edited 1 time in total.
Edited the question
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23 Apr 2012, 10:31
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JordanKatz wrote:
This question really should not be difficult, but the explanation given by GMAC seems to violate the rules of operations PEMDAS. sqrt((16)(20)+(16)(16)) simplified to... sqrt((16)(20+16)) I understand eliminating one of the 16s on the right since its essentially 16 squared, but I dont understand why they can then add 20 and 16 BEFORE multiplying by the left-hand 16

i attached a screen shot of OGs explanation

$$\sqrt{16*20+8*32}=$$

A. $$4\sqrt{20}$$

B. $$24$$

C. $$25$$

D. $$4\sqrt{20}+8\sqrt{2}$$

E. $$32$$

Everything is correct there.

$$\sqrt{16*20+8*32}=$$ --> factor out 16: $$\sqrt{16(20+8*2)}=\sqrt{16(20+16)}=\sqrt{16*36}=4*6=24$$.

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23 Apr 2012, 16:45
Got B, but took 2 minutes get the number, I like the math manipulation strategy above, much quicker.
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30 Jul 2013, 05:03
sqrt(4*4*4*5+4*4*4*4)=sqrt(4*4*4*4*9)=2*2*2*3=8*3=24
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19 Aug 2014, 20:00
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19 Aug 2014, 21:57
$$\sqrt{16*20+8*32} = \sqrt{64(5+4)} = \sqrt{64 * 9} = 8*3 = 24$$

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Re: root(16*20+8*32)=   [#permalink] 19 Aug 2014, 21:57
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