Solving Equations with Square Roots #1

Front

What is the general form of a quadratic equation?

Back

The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to solve an equation with square roots?

Back

Solving an equation with square roots involves finding the values of the variable that make the equation true, often by isolating the square root and squaring both sides.

Front

What are the steps to solve the equation x^2 = k?

Back

1. Isolate x^2 on one side of the equation. 2. Take the square root of both sides. 3. Consider both the positive and negative roots.

Front

What is the square root of a number?

Back

The square root of a number x is a value y such that y^2 = x. It can be positive or negative.

Front

How do you check if your solutions to a square root equation are correct?

Back

Substitute the solutions back into the original equation to verify if both sides are equal.

Front

What are the solutions to the equation x^2 = 49?

Back

The solutions are x = 7 and x = -7.

Front

What is the relationship between squaring a number and taking its square root?

Back

Squaring a number and taking its square root are inverse operations; squaring a number gives a positive result, while taking the square root can yield both positive and negative results.

Front

What is the solution to the equation x^2 = 64?

Back

The solutions are x = 8 and x = -8.

Front

What does the symbol ± mean in mathematics?

Back

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

Front

How do you solve the equation x^2 = 9?

Back

Take the square root of both sides to find x = 3 and x = -3.