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

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Math Expert
Joined: 02 Sep 2009
Posts: 60627
x and y are positive integers. Is x^0.5*y^0.5 an integer?  [#permalink]

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04 Nov 2019, 03:26
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45% (medium)

Question Stats:

54% (01:38) correct 46% (02:00) wrong based on 46 sessions

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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

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Joined: 02 Aug 2009
Posts: 8335
Re: x and y are positive integers. Is x^0.5*y^0.5 an integer?  [#permalink]

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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

E
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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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