Solving Radical Equations

Front

What is a radical equation?

Back

A radical equation is an equation in which a variable is contained within a radical (square root, cube root, etc.).

Tags

CCSS.HSA.REI.A.2

Front

How do you isolate a radical in an equation?

Back

To isolate a radical, you can move all other terms to the opposite side of the equation, leaving the radical alone on one side.

Tags

CCSS.HSA.REI.A.2

Front

What is the first step in solving a radical equation?

Back

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

Tags

CCSS.HSA.REI.A.2

Front

What happens when you square both sides of a radical equation?

Back

Squaring both sides eliminates the radical, but it can introduce extraneous solutions that must be checked.

Tags

CCSS.HSA.REI.A.2

Front

What is an extraneous solution?

Back

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

Tags

CCSS.HSA.REI.A.2

Front

How do you check if a solution is valid in a radical equation?

Back

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

Tags

CCSS.HSA.REI.A.2

Front

What is the domain of a radical function?

Back

The domain of a radical function is the set of all input values (x) for which the expression under the radical is non-negative.

Front

What is the square root property?

Back

The square root property states that if x^2 = a, then x = ±√a.

Tags

CCSS.HSA-REI.B.4B

Front

How do you solve the equation √(x + 3) = 5?

Back

Square both sides: x + 3 = 25, then solve for x: x = 22.

Tags

CCSS.HSA.REI.A.2

Front

What is the importance of checking solutions in radical equations?

Back

Checking solutions is important to ensure that they are not extraneous and truly satisfy the original equation.

Tags

CCSS.HSA.REI.A.2