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Number Properties (Exponents + Roots)

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iil-london
 Post subject: Number Properties (Exponents + Roots)
 Post Posted: Sat Apr 12, 2008 6:47 pm 
sqrt((16)(20)+(8)(32)) =

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

What is the best way to answer this question as quickly and efficiently as possible ?

Thanks.
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Rahul
 Post subject:
 Post Posted: Sun Apr 13, 2008 5:57 pm 
I solved the problem as follows:

=sqrt (16(20+(8)(2))
=sqrt(16(20+16))
=sqrt(16*36)
=4*6
=24
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rfernandez
 Post subject:
 Post Posted: Thu Apr 17, 2008 11:27 pm 
Offline
ManhattanGMAT Staff


Posts: 386
Nice solution, Rahul!

The key to Rahul's approach is to identify perfect square factors that you can "pull out."

Another way to get there is to convert everything to prime factors. Depending on your preferences this may or may not be seen as "the best way to answer" it, as it does require a few more steps.

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)]
2^3*sqrt[5+2^2]
8*sqrt(9)
24

Rey
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