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cube roots (need a help!!!!!!!!!)

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by Brent@GMATPrepNow » Sun May 19, 2013 8:57 am
AJP wrote:now i am asking this how to find cube root of 175616...........
not by prime factorization method

by a new method
It would be nice if you included the answer choices.
On the GMAT, you'd never have to actually calculate the cube root of 175,616.
Instead you could either use the answer choices to your advantage. Or you could estimate.

Here's one way to estimate.

cuberoot(175,616) is close to cuberoot(175,000)
cuberoot(175,000) = cuberoot(175 x 1000)
= cuberoot(175) x cuberoot(1000)
= cuberoot(175) x 10

Let's examine cuberoot(175)
Since cuberoot(125) = 5 and cuberoot(216) = 6, we know that cuberoot(175) = 5.something

So, we get ...
cuberoot(175 x 1000) = cuberoot(175) x cuberoot(1000)
= 5.something x 10
= fifty something.
The real value is 56

We could also have used some number sense to see that the units digit of cuberoot(175,616) must be 6 (since 6x6x6 = some value with 6 as units digit)

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Atekihcan » Mon May 20, 2013 12:33 am
As 175616 is 6-digit integer, the cube root of this number must be 2-digit integer (assuming the cube root is an integer, even if the cube root is not integer, the integral part of the cube root must be 2-digit integer. But if the cube root is not integer, calculating exact cube root is beyond the scope and intention of GMAT.)

Now, next step is to guess the cube root with simple 2-digit integers like 30, 40, 50, ... etc.
30³ = 27000 < 175616
40³ = 64000 < 175616
50³ = 125000 < 175616
60³ = 216000 > 175616

So, cube root of 175616 must be between 50 and 60.
Now, the unit's digit of the cube root must be 6 as the unit's digit of 175616 is 6)

So, the cube root must be 56.
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