[tex]a)\ \ \sqrt{8^2+6^2+4^2+2^2+1^2}=\sqrt{64+36+16+4+1}=\sqrt{121}=11\\\\\\b)\ \ (\sqrt[3]{343}-\sqrt[3]{\sqrt{729}})^3=(7-\sqrt[3]{27})^3=(7-3)^3=4^3=64\\\\\\c)\ \ \dfrac{6^3}{-3^4-(-3)^4}\cdot\sqrt[3]{3\frac{3}{8}}=\dfrac{216}{-81-3^4}\cdot\sqrt[3]{\frac{27}{8}}=\dfrac{216}{-81-81}\cdot\dfrac{\sqrt[3]{27}}{\sqrt[3]{8}}=\dfrac{216}{-162}\cdot\dfrac{3}{2}=\\\\\\=-\dfrac{216}{162}\cdot\dfrac{3}{2}=-\dfrac{\not4^2}{\not3_{1}}\cdot\dfrac{\not3^1}{\not2_{1}}=-2[/tex]
[tex]d)\ \ \sqrt{\dfrac{1^3+2^3+3^3+4^3+5^3+6^3}{1^3+3^3+5^3+7^3+9^3}}=\sqrt{\dfrac{1+8+27+64+125+216}{1+27+125+343+729}}=\sqrt{\dfrac{441}{1225}}=\\\\\\=\sqrt{\dfrac{441:49}{1225:49}}=\sqrt{\dfrac{9}{25}}=\dfrac{\sqrt{9}}{\sqrt{25}}=\dfrac{3}{5}[/tex]
