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

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Intern
Joined: 23 Apr 2012
Posts: 1

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Updated on: 23 Apr 2012, 10:28
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Difficulty:

15% (low)

Question Stats:

81% (00:55) correct 19% (01:38) wrong based on 185 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

Originally posted by JordanKatz on 23 Apr 2012, 09:35.
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, 21:57
$$\sqrt{16*20+8*32} = \sqrt{64(5+4)} = \sqrt{64 * 9} = 8*3 = 24$$

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26 Aug 2018, 18:23
JordanKatz wrote:
$$\sqrt{16*20+8*32}=$$

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

B. $$24$$

C. $$25$$

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

E. $$32$$

We must first simplify the expression in the square root before actually taking the square root. In other words, we have to get the product of 16 and 20 and add it to the product of 8 and 32 before taking the square root.

√[(16)(20) + (8)(32)]

√(320 + 256)

√576 = 24

Note: If struggling with determining the value of √576, we could have used the answer choices to our advantage. We need to ask ourselves what number, when squared, equals 576. Since we should have the value of 25^2 memorized, we would know that 25^2 = 625. Since 576 is slightly less than 625, we can reasonably determine that 24^2 = 576.
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Re: root(16*20+8*32)= &nbs [#permalink] 26 Aug 2018, 18:23
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