Square Roots and Quadratic Equations

The video tutorial explains how to solve quadratic equations using square roots. It begins with isolating the x squared term and then taking the square root of both sides. The first example demonstrates solving 8x^2 = 648 by dividing both sides by 8 and then taking the square root, resulting in x = ±9. The second example involves solving x^2 = 75 by identifying perfect square factors, simplifying the square root, and finding x = ±5√3. The tutorial emphasizes understanding the process of isolating x squared and simplifying square roots.

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

• Add 5 to both sides

• Multiply both sides by 2

• Subtract 3 from both sides

• Isolate x squared

When solving 8x^2 = 648, what is the result of dividing 648 by 8?

• 72

• 80

• 81

• 64

What is the square root of 81?

• 10

• 9

• 8

• 7

What is the solution for x in the equation x^2 = 81?

• x = 8 or x = -8

• x = 9 or x = -9

• x = 10 or x = -10

• x = 11 or x = -11

What does the square root of x squared equal?

• x

• x cubed

• 2x

• x squared

In the second example, what is the first step when x squared is already isolated?

• Subtract 5 from both sides

• Multiply both sides by 3

• Take the square root of both sides

• Add 10 to both sides

What is the prime factorization of 75?

• 8 x 8 x 0

• 6 x 6 x 2

• 5 x 5 x 3

• 7 x 7 x 1

Which number is a perfect square factor of 75?

• 16

• 25

• 9

• 36

What remains under the square root when simplifying the square root of 75?

• 4

• 5

• 3

• 2

What is the simplified form of the square root of 75?

• 5 square root of 5

• 5 square root of 4

• 5 square root of 3

• 5 square root of 2