Solving Quadratic Equations with Square Roots

The video tutorial explains how to solve quadratic equations using square roots. It covers three examples: solving (X - 5)^2 = 16, (3X + 2)^2 = 81, and (X + 2)^2 = 48. The tutorial emphasizes the importance of including a plus or minus sign when taking square roots to find two solutions. It also discusses the simplification of square roots and the distinction between rational and irrational solutions.

What is the first step in solving a quadratic equation using square roots?

• Subtract a constant from both sides

• Multiply both sides by a constant

• Take the square root of both sides

• Add a constant to both sides

Why do we include a plus or minus sign when taking the square root of both sides?

• To make the equation linear

• To account for both positive and negative roots

• To simplify the equation

• To eliminate the variable

When solving (X - 5)^2 = 16, what are the two possible values for X?

• X = 5 and X = -5

• X = 9 and X = 1

• X = 4 and X = -4

• X = 8 and X = 2

What is the result of adding and subtracting 4 from 5 in the equation (X - 5)^2 = 16?

• X = 8 and X = 2

• X = 7 and X = 3

• X = 6 and X = 4

• X = 9 and X = 1

In the equation (3X + 2)^2 = 81, what is the value of the square root of 81?

• 7

• 8

• 9

• 10

What are the two solutions for X in the equation (3X + 2)^2 = 81?

• X = 4/3 and X = -4/3

• X = 3 and X = -3

• X = 5/3 and X = -5/3

• X = 7/3 and X = -11/3

What is the significance of having two real rational solutions in a quadratic equation?

• The equation can be solved by graphing

• The equation is linear

• The equation can be solved by factoring

• The equation has no solutions

What is the simplified form of the square root of 48?

• 4√3

• 5√3

• 7√3

• 6√3

In the equation (X + 2)^2 = 48, what are the two solutions for X?

• X = -2 ± 4√3

• X = 2 ± 4√3

• X = -2 ± 3√4

• X = 2 ± 3√4

Why can't we add and subtract 4 from -2 in the equation (X + 2)^2 = 48?

• Because 4 is a constant

• Because the equation is not linear

• Because 4 is being multiplied by √3

• Because -2 is a variable