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512^(1/9)

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512^(1/9) [#permalink] New post 10 Feb 2013, 20:10
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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] New post 10 Feb 2013, 20:13
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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] New post 10 Feb 2013, 20:19
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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] New post 10 Feb 2013, 20:35
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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] New post 11 Feb 2013, 08:59
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


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


Thank you for the suggestion. I will add those to my working pile of notecards. :)
Re: 512^(1/9)   [#permalink] 11 Feb 2013, 08:59
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