Solving Equations with Square Roots

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 the equation x² = a?

Back

To solve x² = a, take the square root of both sides: x = ±√a.

Front

What is the solution to the equation x² = 16?

Back

The solutions are x = 4 and x = -4.

Front

How do you isolate x in the equation √x = a?

Back

Square both sides of the equation to eliminate the square root: x = a².

Front

What is the solution to the equation √x = 4?

Back

The solution is x = 16.

Front

What is the solution to the equation √x = 9?

Back

The solution is x = 81.

Front

What does it mean if an equation has no real solutions?

Back

It means that there are no values of x that satisfy the equation, often due to taking the square root of a negative number.

Front

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

Back

Squaring both sides of an equation is a method used to eliminate square roots, but it can introduce extraneous solutions.

Front

What are extraneous solutions?

Back

Extraneous solutions are solutions that emerge from the process of solving an equation but do not satisfy the original equation.

Front

How can you check if a solution is valid?

Back

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