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√(16-20+8-32)=

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√(16-20+8-32)=

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\(\sqrt{16\cdot 20+8\cdot 32}=\)

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

OA=B

Source: Official Guide

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M7MBA wrote:
\(\sqrt{16\cdot 20+8\cdot 32}=\)

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

OA=B

Source: Official Guide
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" (here's the video: http://www.gmatprepnow.com/module/general-gmat-strategies?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, √[(16)(20)+(8)(32)] = √[(16)(20)+(16)(16)]
= √[16(20 + 16)] I factored out the 16
= √[(16)(36)]

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

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

Answer: B

Cheers,
Brent

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Brent Hanneson – Creator of GMATPrepNow.com
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M7MBA wrote:
\(\sqrt{16\cdot 20+8\cdot 32}=\)

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

OA=B

Source: Official Guide
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

Note: If you have trouble determining the value of √576, you could have used the answer choices to your advantage. Ask yourself 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.

Alternate Solution:

Let’s begin by factoring the common factor of 8 under the radical sign:

√[(16)(20) + (8)(32)] = √[8(2*20 + 32] = √[8(40 + 32)]

Next, we factor another 8 from each term in the summation:

√[8(40 + 32)] = √[8*8(5 + 4)] = √[8*8*9] = [√(8*8)] * [√9]

The square root of 8*8 is 8 and the square root of 9 is 3; therefore, the answer is 8 * 3 = 24.

Answer: B

_________________

Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com



See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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