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Square root sums

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Square root sums

by JJMforthegold » 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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by Brent@GMATPrepNow » 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
Brent Hanneson - Creator of GMATPrepNow.com
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by [email protected] » 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

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by Jeff@TargetTestPrep » Thu Apr 05, 2018 10:21 am
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
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

Alternate Solution:

Let's factor out the common factor of 16 under the radical sign:

√[(16)(20) + (8)(32)] = √[(16)(20 + 8*2)] = √[16*36] = 4*6 = 24

Answer: 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.

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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