Answer:
1a. -5
1b. 3
1c. -5i
2. S = 11 m
3. S = 4 ft.
Step-by-step explanation:
1a. ∵ cube root of -125 means ∛(-5)(-5)(-5) = ∛(-5)³
∴ [tex]((-5)^{3})^{\frac{1}{3}}[/tex] = -5
1b. [tex]\sqrt[4]{81}=\sqrt[4]{(3)(3)(3)(3)} =\sqrt[4]{(3)^{4} }=(3^{4})^{\frac{1}{4}}=3[/tex]
1c. [tex]\sqrt[4]{-625}=\sqrt[4]{(-1)(625)}[/tex]
∵ i = [tex]\sqrt[4]{-1}[/tex]
∴ [tex]\sqrt[4]{(-1)(625)}= i \sqrt[4]{5^{4}} =i (5^{4})^{\frac{1}{4} } = 5i[/tex]
2. The volume of the cube = S³
∵ V = 1331 m³
∴ S = ∛1331 = 11 m
3. The volume of the cube = S³
∵ V = 64 ft.³
∴ S = ∛64 = 4 ft.
