Question 849167
{{{sqrt(root(3,125000000000))}}}


{{{sqrt(root(3,125*10^9))}}}


{{{sqrt(root(3,125)*root(3,10^9))}}}


{{{sqrt(root(3,5^3)*root(3,10^9))}}}


{{{sqrt(5*10^(9/3)^"")}}}


{{{sqrt(5*10^3)}}}


{{{sqrt(10^2*5*10)}}}


{{{sqrt(10^2*50)}}}


{{{sqrt(10^2*25*2)}}}


{{{sqrt(10^2*5^2*2)}}}


{{{sqrt((10*5)^2*2)}}}


{{{sqrt(50^2*2)}}}


{{{sqrt(50^2)*sqrt(2)}}}


{{{50*sqrt(2)}}}


=======================================================


So, {{{sqrt(root(3,125000000000)) = 50*sqrt(2)}}}


Using a calculator, we see that <img src="http://www.sciweavers.org/tex2img.php?eq=%5Csqrt%7B%5Csqrt%5B3%5D%7B125%2C000%2C000%2C000%7D%7D%20%5Capprox%2070.7106781186548&bc=White&fc=Black&im=jpg&fs=12&ff=arev&edit=0" align="center" border="0" alt="\sqrt{\sqrt[3]{125,000,000,000}} \approx 70.7106781186548" width="386" height="38" /> (since <img src="http://latex.codecogs.com/gif.latex?\large&space;50\sqrt{2}&space;\approx&space;70.7106781186548" title="\large 10\sqrt{50} \approx 70.7106781186548" /> )