Cube Roots and Properties of Equality

This lesson covers square and cube roots, emphasizing their uniqueness for any positive number. It includes an activity to find rules for these roots and explains the properties of equality in solving equations. The lesson provides steps to solve equations involving roots and offers exercises for practice.

What is the significance of the uniqueness of square and cube roots for positive numbers?

• It allows for the existence of negative roots.

• It is only applicable to whole numbers.

• It ensures that each positive number has exactly one square and one cube root.

• It helps in identifying multiple solutions.

In the 'Find the Rule' activity, how do you determine the number in the second column?

• By dividing the number in the first column by two.

• By subtracting the number in the first column from itself.

• By squaring the number in the first column.

• By adding the number in the first column to itself.

What is the cube root of 64?

• 4

• 5

• 3

• 2

Which property of equality allows you to subtract the same number from both sides of an equation?

• Multiplication property of equality

• Division property of equality

• Subtraction property of equality

• Addition property of equality

What happens when you take the square root of both sides of the equation 25 = 25?

• You get a new equation: 5 = 5.

• You get a false equation.

• The equation remains unchanged.

• The equation becomes 0 = 0.

How do you solve the equation x^2 = 81?

• By subtracting 81 from both sides.

• By taking the square root of both sides.

• By multiplying both sides by 81.

• By adding 81 to both sides.

What is the cube root of 8?

• 1

• 2

• 4

• 3

What is the first step in solving the equation x^2 = 256^-1?

• Rewrite 256^-1 as 1/256.

• Take the square root of both sides.

• Multiply both sides by 256.

• Add 256 to both sides.

What is the positive value of x that satisfies the equation x^3 = 343^-1?

• 1/7

• 7

• 343

• 1/343

Is 6 a solution to the equation x^2 - 4 = 5x?

• No, because it is a negative number.

• Yes, because it is a positive number.

• No, because it does not satisfy the equation.

• Yes, because it satisfies the equation.