1.05 Cube roots of perfect cubes
Evaluate:
Determine whether the following statements true or false:
\sqrt{64} = 8
\sqrt[3]{64} = 4
\sqrt{16} = 4
\sqrt[3]{16} = 2
\sqrt{512} = 16
\sqrt[3]{512} = 8
\sqrt{729} = 27
\sqrt[3]{729} = 94
Evaluate:
Evaluate:
\sqrt[3]{ - 1 }
\sqrt[3]{ - 64 }
\dfrac{1}{\sqrt[3]{8}}
\sqrt[3]{ 27 \cdot 8}
\sqrt[3]{ 243 \cdot 3}
\dfrac{1}{2} \sqrt[3]{ 16 \cdot 4}
\sqrt[3]{ - 125 } \cdot \sqrt[3]{27}
\sqrt[3]{ - 125 } \cdot \sqrt[3]{ - 64 }
Evaluate:
Solve:
Juan knows that x^3=-64 has a solution of -4 but that x^2=-64 has no solution. Explain why this is the case.
Find the side length of a cube with a volume of 8\text{ ft}^3.
A toy block in the shape of a cube has a volume of 8\text{ in}^{3}. What is the length of one side of the block?
Letisha is digging a hole for a pond in her yard. The hole is currently in the shape of a cube and has a volume of 27\text{ ft}^{3}.
What is the length of one side of the hole?
How much wider do the sides need to be for the hole to be in the shape of a cube with a volume of 125\text{ ft}^{3}?