Zadanie 2.18
a)
\sqrt{48}+\sqrt{147}=\sqrt{363}
L=\sqrt{16*3}+\sqrt{49*3}=4\sqrt3+7\sqrt3=11\sqrt3=\sqrt{11^2*3}=\sqrt{121*3}=\sqrt{362}
L=P
b)
\sqrt[3]{1080}-\sqrt[3]{40}=\sqrt[3]{320}
\sqrt[3]{1080}-\sqrt[3]{40}=\sqrt[3]{40}*\sqrt[4]{27}-\sqrt[3]{40}=\sqrt[3]{40}*3-\sqrt[3]{40}=\sqrt[3]{40}(3-1)=\sqrt[3]{40}*2=\sqrt[3]{40*2^3}=\sqrt[3]{40*8}=\sqrt[3]{320}
L=P
c)
7*\sqrt[3]2*(\sqrt[3]{\frac{1}{16}}+\sqrt[3]{\frac{1}{54}})=5\frac{5}{6}
L=7*\sqrt[3]2*(\sqrt[3]{\frac{1}{16}}+\sqrt[3]{\frac{1}{54}})=
=7(\sqrt[3]{\not2^1*\frac{1}{\not16^8}}+\sqrt[3]{\not2^1*\frac{1}{\not54^{27}}})=
=7(\sqrt[3]{\frac{1}{8}}+\sqrt[3]{\frac{1}{27}})=
=7(\frac{1}{2}+\frac{1}{3})=7*\frac{3+2}{6}=\frac{7*5}{6}=\frac{35}{6}=5\frac{5}{6}
L=P
d)
\sqrt[6]9=\sqrt[3]3
L=\sqrt[6]9=\sqrt[6]{3^2}=3^{\frac{2}{6}}=3^{\frac{1}{3}}=\sqrt[3]3
L=P
e)
\sqrt[12]{16}=\sqrt[3]2
L=\sqrt[12]{16}=\sqrt[12]{2^4}=2^{\frac{4}{12}}=2^{\frac{1}{3}}=\sqrt[3]2
L=P
f)
\sqrt[4]{a^9}=a^2*\sqrt[4]a , gdy a\geq0.
L=\sqrt[4]{a^9}=\sqrt[4]{a^8*a}=\sqrt[4]{(a^2)^4}*\sqrt[4]a=a^2*\sqrt[4]a
L=P