∛(328 - 800 - 48) is

Question

∛ (328 - 800 - 48) is

A) Between -4 and -5
B) Between -5 and -6
C) Between -6 and -7
D) Between -7 and -8
E) Less than -8

There are a few different ways to solve this one. 
*Kudos for all correct solutions

Abhishek009 · Answer

∛(328 - 800 - 48) = ∛(-520)

Now,  -8^3 = -512

Think of a number line -520 will lie to the left of -512...

Hence, Answer will be (E)..

AnisMURR · Answer

Here is a detailed answer,

Please don't hesitate if you have any question.

Anis

BrentGMATPrepNow · Answer

Another approach is to use a nice rule that says   ∛ (ab) = ( ∛ a)( ∛ b) 
We'll also recognize that we can factor out an 8 (and we happens to know that  ∛ 8 = 2)

We get:  ∛ (328 - 800 - 48) =  ∛  ∛   
= ( ∛ 8)( ∛ -65)    rule  ]  
= (2)( ∛ -65)

Hmmm, what about ( ∛ -65)?

Well we know that ( ∛ -64) = -4
And we know that ( ∛ -125) = -5
Since -65 lies BETWEEN -64 and -125, we know that ( ∛ -65) lies between -4 and -5
So, let's say that ( ∛ -65) =  -4.something

This means that (2)( ∛ -65) = (2)( -4.something ) = some number that's LESS THAN -8

Answer: E

aroon31400 · Answer

\sqrt{(328 - 800 - 48} = \sqrt{-520}

since -8^3 = -512

\sqrt{-520} is less than \sqrt{- 8}

hence E

damybox · Answer

∛(328 - 800 - 48) = ∛(-520)

the prime factorization of 520 is  2^4*5*7

therefore the expression is equal to  -2*∛(2*5*7)= -2*∛70

as 70 is very close to 64 which is 4^3 the value of ∛70 is a little bit higher than 4

therefore  ∛(328 - 800 - 48)>-2*4  =-8

ANSWER E

JeffTargetTestPrep · Answer

We can start by combining the values in the parenthesis:

∛(328 - 800 - 48) = ∛-520

Since 8^3 = 512 and 9^3 = 729, (-8)^3 = -512 and (-9)^3 = -729. Since -520 is between -729 and -512, ∛-520 is between -9 and -8, and thus ∛-520 is less than -8.

Answer: E

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∛(328 - 800 - 48) is

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