Solving Equations with Square Roots: Part 2 Challenge

The video tutorial explains solving equations using reverse order of operations. It covers solving quadratic equations by removing addition, subtraction, multiplication, and division, and then taking square roots to find both positive and negative solutions. It also demonstrates solving cubic equations by removing operations and taking cube roots, emphasizing that only negative solutions are considered for cube roots.

What is the first step in reversing the order of operations to solve an equation?

• Eliminate addition or subtraction

• Square both sides of the equation

• Eliminate multiplication or division

• Eliminate exponents

After eliminating addition or subtraction, what is the next step?

• Take the square root of both sides

• Cube both sides of the equation

• Eliminate multiplication or division

• Addition or subtraction

What is the result of taking the square root of both sides of the equation?

• X = 2

• X = 4

• X = ±2

• X = ±4

What does the square root operation yield in terms of solution type?

• Only positive solutions

• Only negative solutions

• Both positive and negative solutions

• No real solutions

What verifies that X = 2 and X = -2 are solutions to the equation?

• Both give a result of 18 when plugged into the equation

• Only one gives a result of 17 when plugged into the equation

• Both give a result of 17 when plugged into the equation

• Both give a result of 16 when plugged into the equation

What is the first step in solving a cubic equation?

• Cube both sides of the equation

• Eliminate multiplication or division

• Eliminate the cube root

• Eliminate addition or subtraction

After eliminating multiplication in a cubic equation, what is the value of X cubed?

• X cubed = -1

• X cubed = 1

• X cubed = 4

• X cubed = 0

What is the cube root of -1?

• 1

• -2

• 0

• -1

Why do we not consider a positive solution when taking the cube root in the given example?

• Because the original equation only has a negative solution

• Because the cube root of a negative number is always negative

• Because the cube root operation was incorrectly applied

• Because the cube root of a number can only be positive

What is the final answer when solving the cubic equation in the example?

• X = 2

• X = 0

• X = -1

• X = 1