BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Radicals: sqrt((16)(20)+ ( 8 ) (32))

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 400
Joined: Mon Dec 10, 2007 1:35 pm
Location: London, UK
Thanked: 19 times
GMAT Score:680

Radicals: sqrt((16)(20)+ ( 8 ) (32))

by II » Sat Apr 12, 2008 2:45 pm
sqrt((16)(20)+ ( 8 ) (32)) =

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

What was your logic ?
Thanks.
Last edited by II on Mon May 05, 2008 1:38 am, edited 1 time in total.
Top
Source: — Problem Solving |
Senior | Next Rank: 100 Posts
Posts: 93
Joined: Thu Apr 10, 2008 1:42 pm
Location: Chicago
Thanked: 20 times

Re: Number Properties (Exponents + Roots)

by Musiq » Sat Apr 12, 2008 4:11 pm
II wrote:What was your logic ?
Radicals are always a problem whenever there is addition or subtraction involved.

For example: sqrt( ( 4+4) is NOT equal to sqrt (4) + sqrt (4). GMAT/GRE both test us on this common misconception.

On the other hand, if we did have multiplication or division under the radical , that makes it pretty easy.
For example: sqrt( 36 x 81) = sqrt (36) x sqrt (81).

Thats why the logic in any radical problems with addition and subtraction is to convert those mathematical operations to multiplication and division.

Factorization is one of the best tools for this.

Back to Question:
II wrote:sqrt((16)(20)+(8 )(32)) =

(A) 4 sqrt(20)
(B) 24
(C) 25
(D) 4 sqrt(20) + 8 sqrt(2)
(E) 32
sqrt((16)(20)+(8 )(32)) = ???

Since there is addition, be on the lookout for avoiding the obvious trap D

Lets factorise the part inside the radical thusly:
(16) (20) + (8 ) (32) = 16 (20) + (8 ) (2) (16)
This boils down to .......= 16{ (20) + (8 ) (2) }
which then simplifies to = (16) {20+16} = (16) (36)

This is under the radical though. Voila! You have made addition look like Multiplication.

The answer is sqrt { (16) (36)} = sqrt (16) x sqrt (36) = 4x 6 = 24

Qa = B
For love, not money.
Top
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pm
Location: Toronto
Thanked: 1710 times
Followed by:614 members
GMAT Score:800

by Stuart@KaplanGMAT » Sat Apr 12, 2008 7:03 pm
The above solution is 100% correct. Of course, we also could have just done some arithmetic.

sqrt((16)(20)+(8)(32)) = sqrt(320 + 256) = sqrt(576) = 24

choose (b).
Last edited by Stuart@KaplanGMAT on Sun Apr 13, 2008 7:38 am, edited 1 time in total.
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Senior | Next Rank: 100 Posts
Posts: 93
Joined: Thu Apr 10, 2008 1:42 pm
Location: Chicago
Thanked: 20 times

by Musiq » Sat Apr 12, 2008 9:12 pm
Stuart Kovinsky wrote:The above solution is 100% correct. Of course, we also could have just done some arithmetic.

sqrt((16)(20)+(8)(32)) = sqrt(320 + 256) = sqrt(576) = 24

choose (b).
Just for kicks sake Stuart:

The part inside the square root is a number that ends in 6 (since 16x20 + 8x32) yields a units digit that looks like (0 +6).

That leaves only a number ending in 6 or 4 as the answer, since 6^2 = 36 and 4^2 = 16...last digit is 6.

No numbers ending in 6, so only 24 is the answer.

At this point, I am just being more silly than serious though. :D
For love, not money.
Top
Senior | Next Rank: 100 Posts
Posts: 58
Joined: Wed Apr 16, 2008 5:51 pm

by gmat765 » Wed Apr 16, 2008 7:00 pm
sqrt((16)(20)+(Cool(32)) = What does the Cool denote?
Top
Senior | Next Rank: 100 Posts
Posts: 46
Joined: Wed Apr 16, 2008 9:01 pm

by hillzheng » Wed May 14, 2008 4:51 pm
Thanks, Stuart
Top
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Sun May 10, 2015 5:11 pm

by ManifestDestiny88 » Fri May 29, 2015 1:15 pm
"sqrt(576) = 24" is a bad answer because the average test taker does not have that memorized.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Fri May 29, 2015 1:37 pm
sqrt[(16)(20)+(8)(32)]
One option here is to evaluate (16)(20)+(8)(32), and then find the square root of the result. That's a bit of work.

We can also apply a technique called "Multiplying by Doubling and Halving"
We have a free video on this: https://www.gmatprepnow.com/module/gener ... es?id=1113

In the first part, (16)(20), I notice that 16 is a perfect square. Nice!
In the second part, (8)(32), I notice that we have no perfect squares. However, using the doubling and halving technique, we can see that (8)(32) = (16)(16)

So, sqrt[(16)(20)+(8)(32)] = sqrt[(16)(20)+(16)(16)]
= sqrt[16(20 + 16)] {I factored out the 16}
= sqrt[(16)(36)]

At this point, we can apply a useful rule: sqrt(xy) = [sqrt(x)][sqrt(y)]

sqrt[(16)(36)] = [sqrt(16)][sqrt(36)]
= (4)(6)
= 24

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Wed May 06, 2015 10:50 am
Thanked: 1 times

by John@GMATPrepNow » Sat May 30, 2015 12:56 pm
"sqrt(576) = 24" is a bad answer because the average test taker does not have that memorized.
ManifestDestiny88 - I think you are correct. The average test taker wouldn't know that the square root of 576 is 24, but who wants to be the average test taker!?

I have all my students memorize squares up to 25, powers of 2, 3, 5, and 7, fraction decimal equivalents, etc. You should never underestimate the power of math facts. Being "friends with the integers" will allow you to grind through a problem like this quickly and efficiently without worrying about the "best" way to do the problem.

The GMAT rewards knowing these facts:
  • Almost all exponential growth problems are doubling problems. If the population of GMAT students doubles every year for 8 years, and you know that 2^8 = 256, then you're going to find the answer in less than 30 seconds

    2^10 is a good approximation for 1000

    When calculating by hand fractions are almost always better than decimals, so knowing your fractions decimal equivalents will simplify nasty calculations
These are just a few examples.

I've attached a pdf with all the math facts that I think are worth knowing. The list is extensive, but the payoff is worth the work.
Attachments
Math Facts Summary.pdf
(503.23 KiB) Downloaded 199 times
GMAT Prep Now has plans to suit every learning style and budget:
- Self-directed video course
- Private online tutoring from 99th-percentile experts
- Combination packages with video course & private tutoring
- Every plan includes 5 full-length practice tests
- Use our video course along with Beat The GMAT's free 60-Day Study Guide
- We have dozens of free videos to try out before buying

Image
Top
Legendary Member
Posts: 518
Joined: Tue May 12, 2015 8:25 pm
Thanked: 10 times

by nikhilgmat31 » Mon Jun 01, 2015 11:25 pm
Factor to the common variables :)
Top
Master | Next Rank: 500 Posts
Posts: 447
Joined: Fri Nov 08, 2013 7:25 am
Thanked: 25 times
Followed by:1 members

by Mathsbuddy » Tue Jun 02, 2015 7:10 am
I like your answer. Nice and simple.
Musiq wrote:
Stuart Kovinsky wrote:The above solution is 100% correct. Of course, we also could have just done some arithmetic.

sqrt((16)(20)+(8)(32)) = sqrt(320 + 256) = sqrt(576) = 24

choose (b).
Just for kicks sake Stuart:

The part inside the square root is a number that ends in 6 (since 16x20 + 8x32) yields a units digit that looks like (0 +6).

That leaves only a number ending in 6 or 4 as the answer, since 6^2 = 36 and 4^2 = 16...last digit is 6.

No numbers ending in 6, so only 24 is the answer.

At this point, I am just being more silly than serious though. :D
Top
Master | Next Rank: 500 Posts
Posts: 447
Joined: Fri Nov 08, 2013 7:25 am
Thanked: 25 times
Followed by:1 members

by Mathsbuddy » Tue Jun 02, 2015 7:18 am
Rewriting as products of prime factors we get:
(16)(20)+ ( 8 ) (32) = (2x2x2x2)(2x2x5) + (2x2x2)(2x2x2x2x2)
= (2^6 x 5) + (2^6 x 4) = 2^6 x 9
SQRT(2^6 x 9) = 2^3 x 3 = 8 x 3 = 24
Top
Post new topic Post Reply
• Page 1 of 1