1.8 Square Roots

Front

What is a square root?

Back

A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 x 3 = 9.

Front

How do you solve a quadratic equation using square roots?

Back

To solve a quadratic equation in the form ax² + b = 0, isolate x² and then take the square root of both sides. Remember to consider both the positive and negative roots.

Front

What is the square root of 25?

Back

5

Front

What is the principle of squaring a number?

Back

Squaring a number means multiplying the number by itself. For example, 4 squared (4²) is 16.

Front

If x² = 36, what are the possible values of x?

Back

x = 6 or x = -6.

Front

What does it mean if a quadratic equation has no real number solution?

Back

It means that the equation does not intersect the x-axis, and the solutions are complex or imaginary numbers.

Front

How can you represent the height of an object in free fall?

Back

The height can be represented by a quadratic equation, typically in the form h = -16t² + h₀, where h₀ is the initial height.

Front

What is the formula to find the roots of a quadratic equation?

Back

The roots can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

Solve for k: k² - 6 = 43.

Back

k = 7 or k = -7.

Front

What is the height of a water balloon dropped from 80 feet after 2 seconds?

Back

Using the equation h = -16t² + 80, at t = 2, h = -16(2)² + 80 = 16 feet.