dripto biswas Posted January 17, 2013 Share Posted January 17, 2013 WHEN I ENTER ANY NUMBER GREATER THAN 1 IN A CALCULATOR AND KEEP SQUARE ROOTING THE SQUARE ROOT OF THE NUMBER, I WILL OBTAIN 1. ALSO IF THE SAME IS APPLIED TO ANY NUMBER GREATER THAN 0 BUT LESS THAN 1, THE RESULT IS 0.999999............. TO INFINITY. WT IS THE CAUSE AND IMPLICATION OF THESE RESULTS. PLEASE TELL ME AS SOON AS U CAN Link to comment Share on other sites More sharing options...
x(x-y) Posted January 17, 2013 Share Posted January 17, 2013 (edited) If you square root a number, let's call it x where x > 0, and then square root it again - notice that you will obtain [latex]\sqrt{\sqrt{x}} = \left(x^{\frac{1}{2}}\right)^{\frac{1}{2}} = x^{\frac{1}{4}}[/latex] so, if you perform the square root on this variable x an "infinite amount of times" then you will obtain the term [latex]x^{\frac{1}{\infty}} = x^0 = 1[/latex] Thus, we can say that [latex]\displaystyle \lim_{n \to \infty} x^{\frac{1}{n}} = x^0 = 1[/latex] Edited January 17, 2013 by x(x-y) 1 Link to comment Share on other sites More sharing options...
mathematic Posted January 17, 2013 Share Posted January 17, 2013 WHEN I ENTER ANY NUMBER GREATER THAN 1 IN A CALCULATOR AND KEEP SQUARE ROOTING THE SQUARE ROOT OF THE NUMBER, I WILL OBTAIN 1. ALSO IF THE SAME IS APPLIED TO ANY NUMBER GREATER THAN 0 BUT LESS THAN 1, THE RESULT IS 0.999999............. TO INFINITY. WT IS THE CAUSE AND IMPLICATION OF THESE RESULTS. PLEASE TELL ME AS SOON AS U CAN The difference is an artifact of the calculator. .99999....... = 1. 1 Link to comment Share on other sites More sharing options...
dripto biswas Posted February 14, 2013 Author Share Posted February 14, 2013 loved the answers Link to comment Share on other sites More sharing options...
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