In this section, you will be solving equations containing square roots.

Steps for solving equations containing square roots

  1. Isolate the square root on one side of the equation.
  2. Square BOTH sides of the equation.
    The inverse of a square root is squaring. To "undo" a square root you have to square it.
  3. Simplify and solve the equation.
  4. You MUST check your answer(s) to make sure they make the original equation true.
    There may be an extraneous root when both sides were squared.

Example: Solve the equation √x = 5

Step 1: Isolate the square root on one side of the equation. The square root is already on one side of the equation.

√x =
5
Step 2: Square BOTH sides of the equation.
(√x)2 =
(5)2

Step 3: Simplify and Solve.

x =

25

Step 4: Check your answer to see if it makes the original equation true. 		   
√x = 5 ⇒ Does √25 = 5 ⇒ 5 = 5 YES it is true!
So, the final answer is x = 25.

It is really important that you check your answers, especially for square root equations. Sometimes you may get an answer, assume it’s correct, and it does not make the equation true.

Example: Solve the equation √x − 10 = -3

Step 1: Isolate the square root on one side of the equation. The square root is already on one side of the equation.

√x =
7
Step 2: Square BOTH sides of the equation.
(√x)2 =
(7)2

Step 3: Simplify and Solve

x =

49

Step 4: Check answer to make sure it makes the original equation true. 		   
√x − 10 = -3 ⇒ Does √49 − 10 = -3 ⇒ 7 − 10 = -3 YES it is true!
So, the final answer is x = 49.

Remember that any time you square a number it becomes positive, like (3)2=9 or (-4)2=16. However, if a negative sign is in FRONT of parentheses it is NOT included when squaring and then the answer is negative, like -(5)2= -25, because it really means -(5*5) which is -25.

 

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Solve the equation √x  + 8 = 2. Click on the blanks to reveal the answer.

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