Mart Posted October 13, 2005 Share Posted October 13, 2005 Are there any numbers with 2, 3, 7 or 8 in the units place that have rational square roots? Link to comment Share on other sites More sharing options...

timo Posted October 13, 2005 Share Posted October 13, 2005 What is "2, 3, 7, or 8 in the units"? Do you mean as a digit? 121. Do you mean as a prime factor? 4. Something else? Dunno. Link to comment Share on other sites More sharing options...

CanadaAotS Posted October 13, 2005 Share Posted October 13, 2005 I think you mean is any root of x other then actual squares (4, 9, 16 etc.) create a rational number, and the answer is no. All numbers that arent perfect squares produce irrational numbers when square rooted. Link to comment Share on other sites More sharing options...

cosine Posted October 13, 2005 Share Posted October 13, 2005 I'm pretty sure the op meant is there any perfect square with a 2, 3, 7, or 8 in the units place a.k.a. the ones place. As for the question itself, imagine doing the calculation by the "long multiplication" method. Consider doing it with both numbers being equal. We can agree that the units digit of the result must be equal to the units digit of the product of the units digit of the number being squared. Since there are only 10 possible digits in the units place of the number to be squared, there are a finite amount of possiblities to consider. Namely, the squares of the 10 digits, namely: 0, 1, 4, 9, 16, 25, 36, 49, 64, 81. The units digits of these numbers are only 0, 1, 4, 5, 6, and 9. Thus showing that there are no perfect squares with a units digit of 2, 3, 7, or 8. Hope this helps. Link to comment Share on other sites More sharing options...

Mart Posted October 14, 2005 Author Share Posted October 14, 2005 Thanks Cosine. That's what I needed. Link to comment Share on other sites More sharing options...

BigMoosie Posted October 14, 2005 Share Posted October 14, 2005 Are there any numbers with 2, 3, 7 or 8 in the units place that have rational square roots? Yes there are: [math]\sqrt{2.25} = 1.5[/math] [math]\sqrt{3.24} = 1.8[/math] [math]\sqrt{7.29} = 2.7[/math] [math]\sqrt{8.41} = 2.9[/math] Though you may not have worded yuor question correctly if you are after natural numbers. Link to comment Share on other sites More sharing options...

Dave Posted October 14, 2005 Share Posted October 14, 2005 I think the implication was probably natural numbers. Link to comment Share on other sites More sharing options...

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