Understanding Perfect Squares and Solving Quadratic Equations

This video tutorial introduces perfect squares and demonstrates solving quadratic equations by extracting square roots. It covers both perfect and non-perfect square numbers, providing examples and step-by-step solutions. The tutorial also includes complex quadratic examples and advanced methods for solving them. The video concludes with a call to action for viewers to engage with the channel.

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

• Subtract a constant from both sides

• Multiply both sides by a constant

• Get the square root of both sides

• Add a constant to both sides

Which of the following is a perfect square?

• 64

• 75

• 90

• 50

If x^2 = 169, what are the possible values of x?

• 15 and -15

• 12 and -12

• 13 and -13

• 14 and -14

What is the square root of 75 expressed in simplest radical form?

• 3√5

• √75

• 5√3

• 15

Which of the following is a factor of 80 that is a perfect square?

• 9

• 16

• 25

• 36

In the equation 2(x - 5)^2 = 32, what is the value of x after solving?

• x = 6 or x = 4

• x = 9 or x = 1

• x = 8 or x = 2

• x = 7 or x = 3

What is the first step in solving 3(4x - 1)^2 - 1 = 11?

• Subtract 1 from both sides

• Divide both sides by 3

• Multiply both sides by 3

• Add 1 to both sides

What is the simplified form of the square root of 18?

• 6

• √18

• 2√3

• 3√2

In the equation 2(5x + 2)^2 = 64, what is the value of x after solving?

• x = -2 + 4√2/5 or x = -2 - 4√2/5

• x = -3 + 3√2/5 or x = -3 - 3√2/5

• x = -1 + 5√2/5 or x = -1 - 5√2/5

• x = 0 + 6√2/5 or x = 0 - 6√2/5

What is the simplified form of the square root of 32?

• 4√2

• 2√4

• 8

• √32