4th root of 40,000

14.1421356 is the answer

The forth root is a power of a quarter.

$${{\mathtt{40\,000}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{4}}}}\right)} = {\mathtt{14.142\: \!135\: \!623\: \!730\: \!950\: \!5}}$$

Zegroes, you need to show people how you get your answers or else they learn nothing!

the forth root of 40000? $$\sqrt[4]{40000}=\;?$$

$$\sqrt[4]{40000}=$$

$$\\=\sqrt[2]{\sqrt[2]{40000}}\qquad 40000 = 4 * 100 * 100=2*2*100*100=2^2*100^2\\\\ =\sqrt[2]{\sqrt[2]{2^2*100^2}}\\\\ =\sqrt[2]{\sqrt[2]{2^2}\times\sqrt[2]{100^2}}\\\\ =\sqrt[2]{2*100}\qquad 2*100= 2 * 10 * 10=2*10^2 \\\\ =\sqrt[2]{2*10^2}\\\\ =\sqrt[2]{2}\times\sqrt[2]{10^2}}\\\\ =\sqrt2*10\\\\ =10\sqrt2$$

Latex code:

 \\=\sqrt[2]{\sqrt[2]{40000}}\qquad 40000 = 4 * 100 * 100=2*2*100*100=2^2*100^2\\\\
=\sqrt[2]{\sqrt[2]{2^2*100^2}}\\\\
=\sqrt[2]{\sqrt[2]{2^2}\times\sqrt[2]{100^2}}\\\\
=\sqrt[2]{2*100}\qquad 2*100= 2 * 10 * 10=2*10^2
=\sqrt[2]{2*10^2}\\\\
=\sqrt[2]{2}\times\sqrt[2]{10^2}}\\\\
=\sqrt2*10\\\\ 
=10\sqrt2

$$\sqrt[4]{40000}=$$   $${\mathtt{10}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{2}}}} = {\mathtt{14.142\: \!135\: \!623\: \!730\: \!950\: \!5}}$$