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

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Math Expert
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03 Sep 2012, 06:00
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18
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15% (low)

Question Stats:

79% (01:08) correct 21% (01:45) wrong based on 1490 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

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03 Sep 2012, 06:01
2
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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: $$\sqrt{16*20+8*32}=\sqrt{16(20+8*2)}=\sqrt{16*36}=4*6=24$$.

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03 Sep 2012, 06:14
1
$$\sqrt{16*20+8*32}=\sqrt{16*(1*20+8*2)}=4*\sqrt{36}=4*6=24$$

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03 Sep 2012, 07:56
2
\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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04 Sep 2012, 03:39
1
\sqrt{576} = 24
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14 Oct 2012, 08:05
1
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 ??
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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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15 Oct 2012, 03:02
4
asveaass wrote:
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 ??

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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15 Oct 2012, 11:12
asveaass wrote:
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 ??

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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25 Mar 2014, 02:19
Factor out 64 which is a perfect square

$$\sqrt{64 * (5 + 4)}$$

$$\sqrt{64 * 9}$$

8 * 3 = 24 = Answer = B
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28 Feb 2015, 18:15
why can't you factor out a 4? it doesnt work when I do it.
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28 Feb 2015, 18:52
Hi soniasawhney,

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.

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Current Student Joined: 14 Oct 2013 Posts: 45 Re: Root of (16*20+8*32)= [#permalink] ### Show Tags 01 Mar 2015, 13:27 This is how I was doing it.. 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 Let me know if that makes sense! EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12226 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Root of (16*20+8*32)= [#permalink] ### Show Tags 01 Mar 2015, 14:52 2 Hi soniasawhney, 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.... Root[(16)(20) + (8)(32)] Root[16[(20) + (8)(2)] Root[16[(20) + 16]] Root[16[36]] 4(6) = 24 GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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14 Aug 2015, 20:58
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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15 Aug 2015, 04:18
faizanswx wrote:
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

What post are you referring to?

Look at it this way:

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

= $$4*6$$ = 24

Hope this helps.
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15 Aug 2015, 10:11
Hi faizanswx,

When dealing with radicals, you should look for 'perfect squares' (re: 4, 9, 16, 25, etc.) that you can factor-out of the radical...

eg. √50 = √(25x2) = 5√2

In the given prompt, 16 can be factored-out (it becomes '4') and then the 36 can factored-out (it becomes '6').

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31 Oct 2015, 23:43
Ok, this problem is completely baffling the crap out of me! lol!!

Let me first state an assumption I made when doing this problem:

Step 1: Sqrt [(16*20)+(8*32)]= sqrt(16*20) + sqrt(8*32)

Step 2: Sqrt (16*20) = 4*Sqrt(20) = is atleast 16 & sqrt(8*32) = 16

So how in the world is this answer not atleast 32 (I know 32 is not in the answer choice) ? or did I make a big mistake in step 1?
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01 Nov 2015, 02:08
EricImasogie wrote:
Ok, this problem is completely baffling the crap out of me! lol!!

Let me first state an assumption I made when doing this problem:

Step 1: Sqrt [(16*20)+(8*32)]= sqrt(16*20) + sqrt(8*32)

Step 2: Sqrt (16*20) = 4*Sqrt(20) = is atleast 16 & sqrt(8*32) = 16

So how in the world is this answer not atleast 32 (I know 32 is not in the answer choice) ? or did I make a big mistake in step 1?

You should brush-up fundamentals before attempting the questions.

Generally $$\sqrt{a+b}\neq \sqrt{a} + \sqrt{b}$$. For example, $$(\sqrt{4+4}=\sqrt{8})\neq (\sqrt{4} + \sqrt{4}=4)$$.

Theory on Exponents: math-number-theory-88376.html
Tips on Exponents: exponents-and-roots-on-the-gmat-tips-and-hints-174993.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

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01 Nov 2015, 11:33
Root of (32*10+8*32)
=> Root of (32*18)
=> Root of (16*2*2*9)
=> 4*2*3 = 24
Re: Root of (16*20+8*32)= &nbs [#permalink] 01 Nov 2015, 11:33

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