Zadanie 5
a) 3\sqrt{20}+\sqrt5=3\sqrt4*\sqrt5+\sqrt5=\sqrt5(3\sqrt4+1)=\sqrt5(3*2+1)=7\sqrt5
b)
{\sqrt[3]{88}-\sqrt[3]{11}=\sqrt[3]{11}*\sqrt[3]8-\sqrt[3]{11}=\sqrt[3]{11}(\sqrt[3]8-1)=\sqrt[3]{11}(2-1)=\sqrt[3]{11}*1=\sqrt[3]{11}}
Zadanie 6
a)
\sqrt2(\sqrt8+\sqrt{50})=\sqrt{2*8}+\sqrt{2*50}=\sqrt{16}+\sqrt{100}=4+10=14
b)
\sqrt[3]{10^6}=\sqrt[3]{(10^2)^3}=10^2=100
Zadanie 7
a)
{3^4-\frac{3^4\sqrt5}{\sqrt{125}}=3^4-3^4*\sqrt{\frac{5}{125}}=3^4(1-\sqrt{\frac{1}{25}})=3^4(1-\frac{1}{5})=3^4*(\frac{5}{5}-\frac{1}{5})=81*\frac{4}{5}=\frac{324}{5}=64,8}
Zadanie 8
9\ < \sqrt{n} \ < 10 / |^2 wszystkie liczby do kwadratu …n\geq0
81 \ < n < 100
n \textgreater 81 i n < 100
Przykład liczby n: 82 bo 9<\sqrt{82}<10
99-81=18
Jest 18 takich liczb:
{82,83,84,85,86,87, 88, 89, 90, 91,92,93,94,95,96,97,98,99}