SQUARE ROOT RESULT

[dripto biswas]

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

[x(x-y)]

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)

[mathematic]

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.

[dripto biswas]

loved the answers