Root of (16*20+8*32)=

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Root of (16*20+8*32)= [#permalink]

03 Sep 2012, 06:00

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22% (01:39) wrong

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The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

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

(A) 4\sqrt{20}
(B) 24
(C) 25
(D) 4\sqrt{20}+8\sqrt{2}
(E) 32

Practice Questions
Question: 35
Page: 156
Difficulty: 600

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Re: Root of (16*20+8*32)= [#permalink]

03 Sep 2012, 06:01

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SOLUTION

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

(A) 4\sqrt{20}
(B) 24
(C) 25
(D) 4\sqrt{20}+8\sqrt{2}
(E) 32

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

Answer: B.
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Re: Root of (16*20+8*32)= [#permalink]

03 Sep 2012, 06:14

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\sqrt{16*20+8*32}=\sqrt{16*(1*20+8*2)}=4*\sqrt{36}=4*6=24

Answer B.

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Re: Root of (16*20+8*32)= [#permalink]

03 Sep 2012, 07:56

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\sqrt{4*4*4*5 + 4*4*4*4} = 2*2*2\sqrt{5+4} = 8*\sqrt{9} = 8*3 = 24

B
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Re: Root of (16*20+8*32)= [#permalink]

04 Sep 2012, 03:39

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\sqrt{576} = 24
B is the right answer.
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Re: Root of (16*20+8*32)= [#permalink]

07 Sep 2012, 05:23

SOLUTION

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

(A) 4\sqrt{20}
(B) 24
(C) 25
(D) 4\sqrt{20}+8\sqrt{2}
(E) 32

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

Answer: B.

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Re: Root of (16*20+8*32)= [#permalink]

14 Oct 2012, 08:05

Obviously I don't get this..... :shock:

I know this must be wrong since no answer choice allows this, but where am I mistaking? Appreciate the help!

Rt (16*20)+(8*32)=
Rt(2^4*2^2*5)+(2^3*2^5)=
2^3 Rt(5)+2^4=
8Rt5+16 ??

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Re: Root of (16*20+8*32)= [#permalink]

14 Oct 2012, 23:47

Quote:

Obviously I don't get this.....

I know this must be wrong since no answer choice allows this, but where am I mistaking? Appreciate the help!

Rt (16*20)+(8*32)=
Rt(2^4*2^2*5)+(2^3*2^5)=
2^3 Rt(5)+2^4=
8Rt5+16 ??

If you find the shortcuts difficult then take the longer method, by which you can still solve it under the recommended time ...

We are to find the Root of 16x20 + 8x32..

16x20 = 320 , and 32 x 8 = 256 .. Adding them we get , 576 So we are to find the root of 576...

4 root 20 cannot be equal to 576 ( in order to get 576 from this root of 20 would have to be 144 which is obviously not possible) SO A IS OUT ..

24 . Multiplying 24 by 24 we get 576 therefore b is the correct answer..
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Re: Root of (16*20+8*32)= [#permalink]

15 Oct 2012, 03:02

asveaass wrote:

Obviously I don't get this..... :shock:

I know this must be wrong since no answer choice allows this, but where am I mistaking? Appreciate the help!

Rt (16*20)+(8*32)=
Rt(2^4*2^2*5)+(2^3*2^5)=
2^3 Rt(5)+2^4=
8Rt5+16 ??

It should be:

\sqrt{16*20+8*32}=\sqrt{2^4*2^2*5+2^3*2^5}=\sqrt{2^6*5+2^8}=\sqrt{2^6(5+2^2)}=\sqrt{2^6*9}=2^3*3=24.

Hope it's clear.
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Re: Root of (16*20+8*32)= [#permalink]

15 Oct 2012, 11:12

asveaass wrote:

Obviously I don't get this..... :shock:

I know this must be wrong since no answer choice allows this, but where am I mistaking? Appreciate the help!

Rt (16*20)+(8*32)=
Rt(2^4*2^2*5)+(2^3*2^5)=
2^3 Rt(5)+2^4=
8Rt5+16 ??

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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Re: Root of (16*20+8*32)= [#permalink] 15 Oct 2012, 11:12

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Root of (16*20+8*32)=

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