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Square root sums

This topic has 2 expert replies and 0 member replies
JJMforthegold Newbie | Next Rank: 10 Posts Default Avatar
Joined
29 Aug 2017
Posted:
5 messages

Square root sums

Post Sun Sep 17, 2017 3:43 pm
Experts-

How are we supposed to handle sums under a square root? Do we split them in pieces or do the sum first? Here is a sample question

√[(16)(20) + (8)(32)] =

a) 4√20
b) 24
c) 25
d) 4√20 + 8√2
e) 32
b

This question is from an old OG. The whole calculation is under the square root.

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GMAT/MBA Expert

Post Tue Sep 19, 2017 2:38 pm
Hi JJMforthegold,

GMAT questions are always specifically designed - the words in the prompt and the number chosen (including the answer choices) are never random. Thus, you can sometimes use the answer choices 'against' the prompt and save some time.

There's clearly a calculation involved in this question, but how you choose to do that calculation might save you some time. To start, it's interesting that 3 of the answer choices are integers - maybe the correct answer IS an integer.

We ultimately want to take the square root of one large number, so what can we quickly figure out about that number...

(16)(20) --> ends in a 0
(8)(32) --> ends in a 6
Thus, the sum of those two values will be an integer that ends in a 6. Would squaring ANY of the five answer choices get you an integer that ended in a 6? Only one of them, so that must be the correct answer.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

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GMAT/MBA Expert

Post Sun Sep 17, 2017 3:48 pm
JJMforthegold wrote:
Experts-

How are we supposed to handle sums under a square root? Do we split them in pieces or do the sum first? Here is a sample question

√[(16)(20) + (8)(32)] =

a) 4√20
b) 24
c) 25
d) 4√20 + 8√2
e) 32
Useful mental math fact: AB = (A/2)(2B)
For example, (8)(15) = (4)(30)
In this example, we see that 16 is a perfect square (which is useful in square root questions), so we can factor it out of (16)(20).
Also, using our nice mental math rule, we can rewrite (8)(32) as (16)(16)


So, here we go....
√[(16)(20) + (8)(32)] = √[(16)(20) + (16)(16)]
= √[16(20 + 16)]
= √[16(36)]
= [√16] [√36]
= (4)(6)
= 24

Cheers,
Brent

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Brent Hanneson – Founder of GMATPrepNow.com
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