Find $\sqrt[3]{-8}$
Find $\sqrt[3]{-27}$
Find $\sqrt[3]{-1728}$
Simplify: $\sqrt[3]{8 \times 27}$
Simplify: $\sqrt[3]{64 \times 125}$
Find: $\sqrt[3]{140 \times 2450}$
Simplify: $\sqrt[3]{108 \div 4}$
Simplify: $\sqrt[3]{512 \div 8}$
The volume of a cube is $2197\text{ cm}^3$. Find the length of its side.
If the volume of a cube is $9261\text{ cm}^3$, find the length of one edge of the cube.
To find a cube root, you are looking for a number that, when multiplied by itself three times, equals the value inside the radical.
$\sqrt[3]{-8} = -2$
Explanation: Since $(-2) \times (-2) = 4$, and $4 \times (-2) = -8$, the cube root of $-8$ is $-2$.
$\sqrt[3]{-27} = -3$
Explanation: Multiplying $-3$ by itself three times: $(-3) \times (-3) \times (-3) = -27$.
$\sqrt[3]{-1728} = -12$
Explanation: Using the fact that $12^3 = 1728$, and since the number is negative, the root must also be negative: $(-12) \times (-12) \times (-12) = -1728$.
This property allows you to combine two roots into one or split one root into two factors to make calculation easier.
Simplify: $\sqrt[3]{8 \times 27} = 6$
Explanation: You can solve this two ways. First, multiply inside: $\sqrt[3]{216} = 6$. Alternatively, find individual roots: $\sqrt[3]{8} \times \sqrt[3]{27} = 2 \times 3 = 6$.
Simplify: $\sqrt[3]{64 \times 125} = 20$
Explanation: Finding the individual cube roots is easier: $\sqrt[3]{64} = 4$ and $\sqrt[3]{125} = 5$. Then, $4 \times 5 = 20$.
Find: $\sqrt[3]{140 \times 2450} = 70$
Explanation: Multiply the numbers: $140 \times 2450 = 343,000$. Since $\sqrt[3]{343} = 7$ and $\sqrt[3]{1000} = 10$, the result is $7 \times 10 = 70$.
Similar to multiplication, you can perform the division inside the radical first.
Simplify: $\sqrt[3]{108 \div 4} = 3$
Explanation: First, divide $108$ by $4$ to get $27$. Then, $\sqrt[3]{27} = 3$.
Simplify: $\sqrt[3]{512 \div 8} = 4$
Explanation: Divide $512$ by $8$ to get $64$. Then, $\sqrt[3]{64} = 4$.
For cubes, the Volume ($V$) is equal to the side length ($s$) cubed ($V = s^3$). To find the side length, you must take the cube root of the volume.
The volume is $2197\text{ cm}^3$. Find the side length.
Answer: 13 cm
Explanation: Calculate $\sqrt[3]{2197}$. Since $10^3 = 1000$ and $20^3 = 8000$, the answer is between $10$ and $20$. Since it ends in $7$, we check $13$: $13 \times 13 \times 13 = 2197$.
The volume is $9261\text{ cm}^3$. Find the edge length.
Answer: 21 cm
Explanation: Calculate $\sqrt[3]{9261}$. Since $20^3 = 8000$, the answer is slightly above $20$. Testing $21$: $21 \times 21 \times 21 = 9261$.