Solving square and cube 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 9 is 3, since 3² = 9.

Front

What is a cube root?

Back

A cube root of a number x is a value y such that y³ = x. For example, the cube root of 27 is 3, since 3³ = 27.

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 an extraneous solution?

Back

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

Front

Solve for x: √(x + 1) = 3. What is x?

Back

x = 8.

Front

Solve for x: √(x - 4) = -2. What is x?

Back

No solution, since a square root cannot be negative.

Front

Solve for x: x³ = 64. What is x?

Back

x = 4.

Front

Solve for x: x² = 16. What are the possible values of x?

Back

x = 4 or x = -4.

Front

What is the principle of squaring both sides of an equation?

Back

Squaring both sides of an equation can help eliminate square roots, but it may introduce extraneous solutions that need to be checked.

Front

How do you check for extraneous solutions?

Back

Substitute the solution back into the original equation to see if it holds true.