the forth root of 40000? 4√40000=?
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
4√40000= 10×√2=14.1421356237309505
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