What is a cube root?

The cube root of a number is a value that, when multiplied by itself three times, gives the original number. For example, the cube root of 27 is 3, since 3 × 3 × 3 = 27.

What is the rule for multiplying cube roots?

To multiply cube roots, multiply the values inside the cube roots and then find the cube root of the result. For example, ∛2 * ∛8 = ∛(2*8) = ∛16 = 2.52 (approximately).

Solve for x: ∛x = 4.

Hint: Cube both sides to eliminate the cube root.

Cube both sides: (∛x)³ = 4³, which simplifies to x = 64.

Solve the equation: ∛(x + 1) = 3.

Hint: Start by cubing both sides to remove the cube root.

Cube both sides: (∛(x + 1))³ = 3³, which simplifies to x + 1 = 27. Subtract 1 from both sides: x = 26.

If a = 3, what is the value of a³ + 2a?

Substituting a = 3, we get a³ + 2a = 3³ + 2(3) = 27 + 6 = 33.

What is the relationship between cube roots and cubic equations?

The cube roots of a number correspond to the solutions of the cubic equation x³ = a, where 'a' is the number whose cube root is being found.

Find the cube root of 64.

The cube root of 64 is 4, since 4 × 4 × 4 = 64.

What is the formula for the volume of a cube?

The volume V of a cube with side length a is given by V = a³.

Solve for y: ∛(y - 5) = 2.

Hint: Cube both sides to solve for y.

Cube both sides: (∛(y - 5))³ = 2³, which simplifies to y - 5 = 8. Adding 5 gives y = 13.

If b = 2, what is the value of 3b³ - 5?

Substituting b = 2, we get 3b³ - 5 = 3(2³) - 5 = 3(8) - 5 = 24 - 5 = 19.

What is the formula for finding the cube of a binomial (a + b)?

The cube of a binomial can be found using the formula: (a + b)³ = a³ + 3a²b + 3ab² + b³. For example, if a = 2 and b = 3, then (2 + 3)³ = 2³ + 3(2²)(3) + 3(2)(3²) + 3³ = 125.

Calculate the value of ∛729.

The value of ∛729 is 9 because 9 × 9 × 9 = 729.