Zadanie 3
a)
\sqrt{18}*\sqrt2:\sqrt6=\frac{\sqrt6*\sqrt3*\sqrt2}{\sqrt6}=\sqrt{3*2}=\sqrt6
b)
\sqrt{2\sqrt{2\sqrt{2{\sqrt4}}}}=\sqrt{2\sqrt{2\sqrt{2*2}}}=\sqrt{2\sqrt{2*2}}=\sqrt{2*2}=\sqrt4=2
c)
\sqrt{36+64}=\sqrt{100}=10
d)
\sqrt{36*64}=\sqrt{36}*\sqrt{64}=6*8=48
e)
(\frac{3\sqrt3}{2})^2=\frac{9*3}{4}=\frac{27}{4}=6\frac{3}{4}=6,75
f)
\sqrt[5]8*\sqrt[15]{64}=8^{\frac{1}{5}}*8^{\frac{1}{15}}*8^{\frac{1}{15}}=8^{\frac{3}{15}+\frac{1}{15}+\frac{1}{15}}=8^{\frac{5}{15}}=8^{\frac{1}{3}}=\sqrt[3]8=2
g)
(2\frac{1}{4})^{-\frac{3}{2}}=(\frac{9}{4})^{-\frac{3}{2}}=(\frac{4}{9})^{\frac{3}{2}}=\frac{(2^2)^{\frac{3}{2}}}{(3^2)^{\frac{3}{2}}}=\frac{2^3}{3^3}=\frac{8}{27}
h)
\sqrt[4]{81*16}=\sqrt[4]{3^4*2^4}=3*2=6
i)
\frac{9^{\frac{1}{3}}*27^{\frac{1}{2}}}{\sqrt3}=\frac{\sqrt[3]9*\sqrt27}{\sqrt3}=\frac{\sqrt[3]9*3\sqrt3}{\sqrt3}=\sqrt[3]9*3=3\sqrt[3]9
j)
\sqrt[4]{4^3}*\sqrt[4]9*\sqrt[4]6=\sqrt[4]{(2^2)^3}*\sqrt[4]{54}=\sqrt[4]{2^4*2^2}*\sqrt[4]{54}=2\sqrt[4]{4*54}=2\sqrt[4]{216}