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x and y are positive integers. Is x^0.5*y^0.5 an integer?

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x and y are positive integers. Is x^0.5*y^0.5 an integer?  [#permalink]

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New post 04 Nov 2019, 03:26
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Re: x and y are positive integers. Is x^0.5*y^0.5 an integer?  [#permalink]

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New post 04 Nov 2019, 05:39
x and y are positive integers. Is \(\sqrt{x}\)*\(\sqrt{y}\) an integer?


(1) \(\frac{x}{y} = \frac{1}{n^2}\)

(2) \(\sqrt[3]{x}*\sqrt[3]{y}\) is an integer

n could be anything so not only statements are individually insufficient but are insufficient combined too..

combined..
x=8, y=8.....
\(\frac{x}{y} =1= \frac{1}{n^2}...n=1.. or....n= -1\)
\(\sqrt[3]{x}*\sqrt[3]{y}=2*2\) is an integer
\(\sqrt{x}\)*\(\sqrt{y}=8\)...Yes
x=8, y=64.....
\(\frac{x}{y} =\frac{8}{64}= \frac{1}{n^2}...n^2=8.. ....n= -2\sqrt{2}...n=2\sqrt{2}\)
\(\sqrt[3]{x}*\sqrt[3]{y}=2*4\) is an integer
\(\sqrt{x}\)*\(\sqrt{y}=\sqrt{8*64}=16\sqrt{2}\)...No

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Re: x and y are positive integers. Is x^0.5*y^0.5 an integer?   [#permalink] 04 Nov 2019, 05:39
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x and y are positive integers. Is x^0.5*y^0.5 an integer?

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