512^(1/9) : GMAT Quantitative Section

512^(1/9)

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512^(1/9) [#permalink]

10 Feb 2013, 21:10

This isn't a full question, I just want to know if there is a quick arithmetic-trick to solving this square root problem?

512^(1/9) = 2

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Re: RE: 512^(1/9) [#permalink]

10 Feb 2013, 21:13

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Factorize 512.
We know that 8^3=512
Also 2^3=8

Hence 2^9=512
Simple

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Re: 512^(1/9) [#permalink]

10 Feb 2013, 21:19

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exploringm wrote:

This isn't a full question, I just want to know if there is a quick arithmetic-trick to solving this square root problem?

512^(1/9) = 2

512 = 256*2 = 16^2*2 = (2^4)^2*2 = 2^8*2 = 2^9

(2^9)^{\frac{1}{9}} = 2^{\frac{9}{9}} = 2
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Re: 512^(1/9) [#permalink]

10 Feb 2013, 21:35

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exploringm wrote:

This isn't a full question, I just want to know if there is a quick arithmetic-trick to solving this square root problem?

512^(1/9) = 2

It will be very helpful if you learn up the first few powers of some numbers.

2^2 to2^{10} i.e. 2^2 = 4, 2^3 = 8, 2^4 = 16 etc
3^2 to3^{6}
4^2 to4^{5}
5^2 to5^{4}
Squares of first 20 positive integers
Cubes of the first 10 positive integers
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Re: 512^(1/9) [#permalink]

11 Feb 2013, 09:59

VeritasPrepKarishma wrote:

exploringm wrote:

This isn't a full question, I just want to know if there is a quick arithmetic-trick to solving this square root problem?

512^(1/9) = 2

Thank you for the suggestion. I will add those to my working pile of notecards.

Re: 512^(1/9) [#permalink] 11 Feb 2013, 09:59

512^(1/9)

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