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

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2
34 00:00

Difficulty:   15% (low)

Question Stats: 80% (01:29) correct 20% (02:21) wrong based on 1502 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

Practice Questions
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Page: 156
Difficulty: 600

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

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8
5
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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Re: Root of (16*20+8*32)=  [#permalink]

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

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

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4
1
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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Re: Root of (16*20+8*32)=  [#permalink]

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why can't you factor out a 4? it doesnt work when I do it.
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Root of (16*20+8*32)=  [#permalink]

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

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This is how I was doing it..

4[(4*5)+(2*8)]
4[20+16]
4
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
take the square root...
2*12=24

Let me know if that makes sense!
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Root of (16*20+8*32)=  [#permalink]

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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]

4(6) = 24

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

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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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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Root of (16*20+8*32)=  [#permalink]

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

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

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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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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Root of (16*20+8*32)=  [#permalink]

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Hi EricImasogie,

While the major Radical rules won't show up too often on Test Day (you'll likely see just 1-2 questions that will involve radical rules), they are a standard part of the GMAT, so if you know the rules, then you should be able to pick up these points.

Since your 'assumptions' about how the math 'worked' were incorrect, I have a few questions about your studies so far:

1) How long have you been studying?
2) What resources have you been using?

It might be that you need some general 'math' practice before you do too much more GMAT practice.

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

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Here is a visual that should help.
Attachments Screen Shot 2016-03-27 at 8.04.32 PM.png [ 105.52 KiB | Viewed 1543 times ]

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

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

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

Solution:

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

The answer is B.

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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Root of (16*20+8*32)=  [#permalink]

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The first thing when you see such questions should be to simplify
16*20 + 8*32 = 320 + 256 = 576
Now, $$\sqrt{576}$$= 24

Correct Option: B

Originally posted by OptimusPrepJanielle on 08 Jun 2016, 20:42.
Last edited by OptimusPrepJanielle on 09 Jun 2016, 02:34, edited 1 time in total.
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Re: Root of (16*20+8*32)=  [#permalink]

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

(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

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

= $$\sqrt{320+256}$$

= $$\sqrt{576}$$

$$24 * 24 = 576$$ , Hence Answer must be (B)
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