zadanie 1
4\sqrt{27}-\sqrt{12}-2\sqrt{75}+\sqrt{108}=
4\sqrt{9*3}-\sqrt{4*3}-2\sqrt{25*3}+\sqrt{36*3}=
4*3\sqrt3-2\sqrt3-2*5\sqrt3+6\sqrt3=
12\sqrt3-2\sqrt3-10\sqrt3+6\sqrt3=6\sqrt3
zadanie 2
V=a^3
{a_1}^3=54
a_1=\sqrt[3]{54}=\sqrt[3]{27*2}
a_1=3\sqrt[3]{2}
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V_2=2
{a_2}^3=2
a_2=\sqrt[3]2
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\frac{a_1}{a_2}=\frac{3\sqrt[3]2}{\sqrt[3]2}=3 <–odpowiedź
albo z podobieństwa:
\frac{V_1}{V_2}=k^3
\frac{54}{2}=k^3
27=k^3
k=\sqrt[3]{27}
k=3