SQUARE ROOT

Here are the steps required for Solving Problems Containing Two Square Roots:

Step 1:Isolate one of the two square roots on one side of the equation by moving all other terms to the opposite side of the equation.
Step 2:Square each side of the equation. Squaring a square root causes one of the square roots to disappear leaving the expression that was inside of the square root.
Step 3:Simplify the equation found in step 2 by distributing (or FOILing) to remove the parenthesis and then combining like terms.
Step 4:At this point, there should only be one square root remaining in the problem. So, isolate the square root by moving all other terms to the opposite side of the equation.
Step 5:Square each side of the equation. Squaring a square root causes the square root to disappear leaving the expression that was inside of the square root.
Step 6:Solve the equation found in step 5. This step may require distributing (or FOILing), combining like terms, isolating the variable, or solving by factoring depending on the remaining terms.
Step 7:Check your answer. When solving square root problems, sometimes you get answers that are not correct, so make sure you plug your answer into the original question to see if it is correct.

Example 1 – Solve: Example 1

Step 1: Isolate one of the two square roots.
Step 1
Step 2: Square each side of the equation.
Step 2
Step 3: Simplify the equation found in step 2. In this case, we need to distribute (or FOIL) to remove the parenthesis and combine like terms. Click on the link below to see how to simplify Simplifying.
Step 3
Step 4: Isolate the remaining square root. In this case, we could divide by 4 because it divides evenly, but I have chosen not to divide.
Step 4
Step 5: Square each side of the equation.
Step 5
Step 6: Solve the equation found in step 5. In this case, we need to isolate the variable.
Step 6
Step 7: Check your answer. When solving square root problems, sometimes you get answers that are not correct, so make sure you plug your answer into the original question to see if it is correct. In this case the correct answer is x = 9 because it checks.
Step 7

Example 2 – Solve: Example 2

Step 1: Isolate one of the two square roots.
Step 1
Step 2: Square each side of the equation.
Step 2
Step 3: Simplify the equation found in step 2. In this case, we need to distribute (or FOIL) to remove the parenthesis and combine like terms. Click on the link below to see how to simplify Simplifying.
Step 3
Step 4: Isolate the remaining square root. In this case, we could divide by 2 because it divides evenly, but I have chosen not to divide.
Step 4
Step 5: Square each side of the equation.
Step 5
Step 6: Solve the equation found in step 5. In this case, we need to distribute and isolate the variable.
Step 6
Step 7: Check your answer. When solving square root problems, sometimes you get answers that are not correct, so make sure you plug your answer into the original question to see if it is correct. In this case the correct answer is x = 15 because it checks.
Step 7

 

Example 3 – Solve: Example 3

Step 1: Isolate one of the two square roots.
Step 1
Step 2: Square each side of the equation.
Step 2
Step 3: Simplify the equation found in step 2. In this case, we need to distribute (or FOIL) to remove the parenthesis and combine like terms. Click on the link below to see how to simplify Simplifying.
Step 3
Step 4: Isolate the remaining square root. In this case, we could divide by 2 or –2, but this would create fractions, so I have chosen not to divide.
Step 4
Step 5: Square each side of the equation.
Step 5
Step 6: Solve the equation found in step 5. In this case, we need to distribute (or FOIL), combine like terms, and then solve by factoring.
Step 6
Step 7: Check your answer. When solving square root problems, sometimes you get answers that are not correct, so make sure you plug your answer into the original question to see if it is correct. In this case the only correct answer is x = 7 because it checks.
Step 7

 

Example 4 – Solve: Example 4

Step 1: Isolate one of the two square roots.
Step 1
Step 2: Square each side of the equation.
Step 2
Step 3: Simplify the equation found in step 2. In this case, we need to distribute (or FOIL) to remove the parenthesis and combine like terms. Click on the link below to see how to simplify Simplifying.
Step 3
Step 4: Isolate the remaining square root. In this case, we could divide by 4, but this would create fractions, so I have chosen not to divide.
Step 4
Step 5: Square each side of the equation.
Step 5
Step 6: Solve the equation found in step 5. In this case, we need to distribute (or FOIL), combine like terms, and then solve by factoring.
Step 6
Step 7: Check your answer. When solving square root problems, sometimes you get answers that are not correct, so make sure you plug your answer into the original question to see if it is correct. In this case the only correct answers are x = 4 or x = 20 because they both check.
Step 7