a)
[tex]\sqrt{9^2+7^2+3^2+2^2+1^2}=\sqrt{81+49+9+4+1}=\\\\=\sqrt{144}=\sqrt{12^2}=12[/tex]
b)
[tex](\sqrt[3]{216}-\sqrt{\sqrt[3]{64}})^3=(\sqrt[3]{6^3}-\sqrt{\sqrt[3]{4^3}})^3=\\\\=(6-\sqrt4)^3=(6-\sqrt{2^2})^3=(6-2)^3=4^3=64[/tex]
c)
[tex]\frac{-3^4-(-3)^4}{6^3}\cdot\sqrt[3]{2\frac{10}{27}}=\frac{-81-81}{216}\cdot\sqrt[3]{\frac{64}{27}}=-\frac{162}{216}\cdot\sqrt[3]{\frac{4^3}{3^3}}=\\\\=-\frac{162}{216}\cdot\frac{4}{3}=-\frac{54}{54}=-1[/tex]
d)
[tex]\sqrt{\frac{1^3+2^3+3^3+4^3+5^3}{1^3+2^3+3^3+4^3+5^3+6^3}}=\sqrt{\frac{1+8+27+64+125}{1+8+27+64+125+216}}=\\\\=\sqrt{\frac{225}{441}}=\sqrt{\frac{15^2}{21^2}}=\frac{15}{21}=\frac{5}{7}[/tex]
