Solving for y in a Cube Root Equation

The video tutorial explains how to solve an equation involving the cube root of y. It begins by isolating the cube root on one side of the equation, then solving for y by dividing both sides by a constant. The solution is verified by substituting back into the original equation to ensure correctness. The tutorial emphasizes understanding the manipulation of equations and verifying solutions.

What is the initial equation given in the problem?

• The cube root of y equals 4 times the cube root of y minus 5.

• The negative of the cube root of y equals 4 times the cube root of y plus 5.

• The square root of y equals 4 times the square root of y plus 5.

• The negative of the square root of y equals 4 times the square root of y plus 5.

What is the first step to isolate the cube root of y?

• Divide both sides by 4.

• Subtract 4 times the cube root of y from both sides.

• Multiply both sides by 5.

• Add 4 times the cube root of y to both sides.

What is the purpose of subtracting 4 times the cube root of y from both sides?

• To simplify the equation to a linear form.

• To make the equation quadratic.

• To eliminate the cube root of y from the equation.

• To isolate the cube root of y on one side.

After isolating the cube root of y, what is the next step?

• Multiply both sides by -5.

• Add 5 to both sides.

• Divide both sides by -5.

• Subtract 5 from both sides.

What does the equation become after dividing both sides by -5?

• The cube root of y equals -1.

• The cube root of y equals 1.

• The cube root of y equals 0.

• The cube root of y equals 5.

What operation is performed to solve for y after isolating the cube root?

• Multiply both sides by 3.

• Raise both sides to the third power.

• Take the fourth root of both sides.

• Square both sides of the equation.

What is the value of y after solving the equation?

• y = 5

• y = -1

• y = 1

• y = 0

How do you verify the solution y = -1?

• By substituting y = -1 into a different equation.

• By substituting y = -1 into the original equation and checking if both sides are equal.

• By checking if y = -1 satisfies a quadratic equation.

• By graphing the equation and finding the intersection point.

What is the cube root of -1?

• 0

• 2

• 1

• -1

What is the result of negative 1 raised to the third power?

• 3

• 1

• -1

• 0