Zadanie 2
a)
\sqrt2+\sqrt{32}+\sqrt{50}=\sqrt2+\sqrt{16*2}+\sqrt{25*2}=\sqrt2+4\sqrt2+5\sqrt2=10\sqrt2
b)
\frac{2*2^{-10}}{2^{-8}}=\frac{2^{1+(-10)}}{2^{-8}}=2^{-9-(-8)}=2^{-1}=\frac{1}{2}
c)
(\sqrt{3}-1)^2*\sqrt[3]{9}*\sqrt[6]{81}=(3-2\sqrt3+1)*(3^2)^{\frac{1}{3}}*(3^4)^{\frac{1}{6}}=
=(4-2\sqrt3)*(3^{\frac{2}{3}}*3^{\frac{2}{3}})=2(2-\sqrt3)*3^{\frac{4}{3}}=2(2-\sqrt3)*3^1*3^{\frac{1}{3}}=6\sqrt[3]{3}(2-\sqrt3)
d)
log_2(log20+log5)=log_2[log(20*5)]=log_2(log100)=log_2(log10^2)=log_22=1
e)
\frac{3}{\sqrt2+1}=\frac{3*(\sqrt2-1)}{(\sqrt2+1)(\sqrt2-1)}=\frac{3(\sqrt2-1)}{2-1}=3(\sqrt2-1)