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# 512^(1/9)

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Intern
Joined: 25 Dec 2012
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10 Feb 2013, 21:10
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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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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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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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10 Feb 2013, 21:35
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Expert's post
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.

$$2^2$$ to$$2^{10}$$ i.e. $$2^2 = 4, 2^3 = 8, 2^4 = 16$$ etc
$$3^2$$ to$$3^{6}$$
$$4^2$$ to$$4^{5}$$
$$5^2$$ to$$5^{4}$$
Squares of first 20 positive integers
Cubes of the first 10 positive integers
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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

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

$$2^2$$ to$$2^{10}$$ i.e. $$2^2 = 4, 2^3 = 8, 2^4 = 16$$ etc
$$3^2$$ to$$3^{6}$$
$$4^2$$ to$$4^{5}$$
$$5^2$$ to$$5^{4}$$
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.

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