Solving Square Root Equations

Front

What is a square root?

Back

A square root of a number x is a value y such that y² = x. For example, the square root of 25 is 5.

Front

How do you solve a square root equation?

Back

To solve a square root equation, isolate the square root on one side and then square both sides of the equation to eliminate the square root.

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 16 is 4.

Front

What does it mean if a square root equation has no solution?

Back

It means that there are no real numbers that satisfy the equation, often occurring when a square root is set equal to a negative number.

Front

Solve the equation: √x = 5.

Back

x = 25.

Front

Solve the equation: √(x + 3) = 7.

Back

x = 46.

Front

What is the first step in solving √(x - 1) = 4?

Back

Square both sides to get x - 1 = 16.

Front

What is the solution to the equation: √(2x + 4) = 6?

Back

x = 14.

Front

How do you check your solution in a square root equation?

Back

Substitute the solution back into the original equation to see if both sides are equal.

Front

What happens when you square both sides of an equation?

Back

You eliminate the square root, but you must check for extraneous solutions afterward.