Solving Square Root Equations

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 the equation x² = 16?

Back

To solve x² = 16, take the square root of both sides. x = ±√16, so x = ±4.

Front

What is the principal square root?

Back

The principal square root is the non-negative square root of a number. For example, the principal square root of 25 is 5.

Front

What does it mean to isolate the variable in an equation?

Back

Isolating the variable means rearranging the equation so that the variable is on one side and all other terms are on the other side.

Front

What is the first step in solving square root equations?

Back

The first step is to isolate the square root on one side of the equation.

Front

How do you check your solution after solving a square root equation?

Back

Substitute your solution back into the original equation to verify that both sides are equal.

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that does not satisfy the original equation, often introduced when squaring both sides of an equation.

Front

Solve the equation √(x + 3) = 5.

Back

Square both sides: x + 3 = 25. Then, isolate x: x = 25 - 3, so x = 22.

Front

What is the square root property?

Back

The square root property states that if x² = a, then x = ±√a.

Front

How do you solve the equation x² - 9 = 0?

Back

Factor the equation: (x - 3)(x + 3) = 0. Thus, x = 3 or x = -3.