1.- Simplifica:

 $\sqrt[\fs13]{x^{\fs1{6}}y^{\fs1{3}}z^{\fs1{9}}}$ $\sqrt[\fs14]{x^{\fs1{4}}y^{\fs1{8}}}$ $\sqrt{\frac{x^2y^4}{z^6}}$ $\sqrt[\fs16]{x^{\fs1{2}}y^{\fs1{6}}z^{\fs1{2}}}$ $\sqrt[\fs15]{\frac{x^{10}y^{20}}{z^{\fs1{10}}}$ $\sqrt[\fs14]{x^{\fs1{12}}y^{\fs1{16}}}$

2.- Extrae del radical todos los factores posibles:

 $\sqrt[\fs13]{81x^{\fs1{3}}y^{\fs1{5}}z}$ $\sqrt[\fs15]{64}$ $\sqrt[\fs1{10}]{x^{\fs1{2}}y^{\fs1{6}}}$ $\sqrt[\fs13]{32x^{\fs1{4}}}$ $\sqrt{(a+b)^{\fs1{2}}x}$ $\sqrt{(a-b)^{\fs1{3}}x^{\fs1{2}}}$ $\sqrt{27(a-b)^{\fs1{3}}}$ $\sqrt[\fs14]{32a^{\fs1{7}}b^{{9}}}$ $\sqrt{12a^{\fs1{3}}b^{\fs1{5}}}$ $\sqrt[\fs14]{a^{\fs1{2}}b^{\fs1{6}}}$ $\sqrt{4x^{\fs1{3}}}$ $\sqrt[\fs17]{5^{\fs1{7}}x^{\fs1{14}}y^{\fs1{3}}z^{\fs1{3}}}$

 $\fs5\frac{\sqrt[\fs13]{3^{\fs1{2}}}\cdot\sqrt[\fs13]{3^{\fs1{5}}\cdot3^{\fs1{-2}}}}{\sqrt[\fs16]{3^{\fs1{-2}}}\,\cdot\sqrt{\sqrt[\fs13]{3^{\fs1{4}}}}}$ $\fs6\frac{\sqrt{x}\cdot\sqrt[\fs15]{x^{\fs1{2}}}\cdot\sqrt[\fs13]{x^{\fs1{6}}}}{\sqrt{x\sqrt[\fs13]{x}}}$ $\fs5\frac{\sqrt{5^{\fs1{3}}\cdot3}\cdot\sqrt[\fs14]{5^{\fs1{2}}\cdot3^{\fs1{2}}}}{\sqrt{3\sqrt[\fs13]{5}}\cdot\sqrt[\fs14]{5}}$ $\fs5\frac{\sqrt{x}\cdot\sqrt{x\sqrt{x}}}{\sqrt[\fs13]{x^{\fs1{2}}}\cdot\sqrt[\fs13]{\sqrt{x}}}$ $\fs4\sqrt{3\sqrt{3\sqrt{3\sqrt{3}}}}$ $\fs4\sqrt[\fs13]{\sqrt[\fs19]{3\sqrt[\fs13]{3}}}$

4.- Calcula:

 $2\sqrt{45}+\sqrt{500}-3\sqrt{245}$ $\sqrt[\fs13]{250}-\sqrt[\fs13]{54}-\sqrt[\fs13]{16}$ $\sqrt{7+5+\sqrt{16}}$ $\fs4\frac13\sqrt{\fs3{27}}-\frac53\sqrt{\frac{48}{9}}+\frac14\sqrt{\frac{75}{9}}$ $\fs4\sqrt{8}-5\sqrt{\frac{18}{25}}+\sqrt{98}$ $\sqrt{32+\sqrt{13+\sqrt{9}}}$ $(\sqrt{8}-3\sqrt{5})^{\fs1{2}}+(\sqrt{8}+3\sqrt{5})^{\fs1{2}}$ $(3\sqrt{7}-2\sqrt{5})\cdot(3\sqrt{7}+2\sqrt{5})$ $\sqrt{20}+3\sqrt{45}-2\sqrt{125}+\frac35\sqrt{180}$ $(2-\sqrt{3})^{\fs1{2}}-(2+\sqrt{3})^{\fs1{2}}$ $\sqrt{23+\sqrt{4}}$ $\sqrt{5+2\sqrt{4}}$ $(-5\sqrt{3}+\sqrt{7})\cdot(5\sqrt{3}+\sqrt{7})$ $\sqrt{6+2\sqrt{25}}$ $\sqrt{\frac29}+\sqrt{\frac{8}{25}}-\sqrt{\frac{2}{225}}$

5.- Racionaliza:

 $\fs4\frac{3}{\sqrt{7}}$ $\fs4\frac{2}{\sqrt{12}}$ $\fs4\frac{6}{\sqrt[\fs13]{2}}$ $\fs4\frac{1}{\sqrt{\sqrt{3}}}$ $\fs4\frac{2}{\sqrt[\fs14]{2}}$ $\fs4\frac{-1}{\sqrt[\fs15]{7^{\fs1{2}}}}$ $\fs4\frac{1}{\sqrt{3}-2\sqrt{3}}$ $\fs4\frac{4}{4-2\sqrt{5}}$ $\fs4\frac{2-\sqrt{5}}{2+\sqrt{5}}$ $\fs4\frac{6}{3\sqrt{2}-2\sqrt{3}}$ $\fs4\frac{1}{3-\sqrt{7}}$ $\fs4\frac{10}{\sqrt{\sqrt{2}}}$