Answer:
Part 5) [tex]3[/tex]
Part 6) [tex]2[/tex]
Par 7) [tex]S=5\ ft[/tex]
Part 8) [tex]S=7\ m[/tex]
Step-by-step explanation:
Part 5) we have
[tex]\sqrt[3]{27}[/tex]
we know that
[tex]27=3^{3}[/tex]
substitute
[tex]\sqrt[3]{27}=\sqrt[3]{3^{3}}=3^{\frac{3}{3}}=3[/tex]
Part 6) we have
[tex]\sqrt[4]{16}[/tex]
we know that
[tex]16=2^{4}[/tex]
substitute
[tex]\sqrt[4]{16}=\sqrt[4]{2^{4}}=2^{\frac{4}{4}}=2[/tex]
Part 7) we know that
The volume of the cube is equal to
[tex]V=S^{3}[/tex]
where
S is the length side of the cube
In this problem we have
[tex]V=125\ ft^{3}[/tex]
substitute
[tex]125=S^{3}[/tex]
[tex]S=\sqrt[3]{125}=\sqrt[3]{5^{3}}=5^{\frac{3}{3}}=5\ ft[/tex]
Part 8) we know that
The volume of the cube is equal to
[tex]V=S^{3}[/tex]
where
S is the length side of the cube
In this problem we have
[tex]V=343\ m^{3}[/tex]
substitute
[tex]343=S^{3}[/tex]
[tex]S=\sqrt[3]{343}=\sqrt[3]{7^{3}}=7^{\frac{3}{3}}=7\ m[/tex]
