Square Root & Complete the Square

Front

What is the square root of a number?

Back

The square root of a number 'x' is a value 'y' such that y² = x. It can be positive or negative.

Front

How do you solve an equation by taking the square root?

Back

To solve an equation by taking the square root, isolate the squared term on one side of the equation and then take the square root of both sides.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, typically in the form (a + b)² = a² + 2ab + b².

Front

How do you create a perfect square trinomial from x² + bx?

Back

To create a perfect square trinomial from x² + bx, take half of 'b', square it, and add it to the expression.

Front

What is the formula for the square root property?

Back

If x² = k, then x = ±√k.

Front

How do you solve the equation x² = 121?

Back

To solve x² = 121, take the square root of both sides to get x = ±11.

Front

What is the significance of the ± symbol in solutions?

Back

The ± symbol indicates that there are two possible solutions: one positive and one negative.

Front

How do you solve the equation 4m² - 100 = 0?

Back

First, isolate m² by adding 100 to both sides, then divide by 4, and finally take the square root to find m = ±5.

Front

What does it mean to complete the square?

Back

Completing the square involves rewriting a quadratic equation in the form (x + p)² = q, making it easier to solve.

Front

How do you solve (x + 6)² = 49?

Back

Take the square root of both sides to get x + 6 = ±7, then solve for x to find x = 1 and x = -13.