How to Solve Radical Equations

Video Tutorial and practice problems

How To solve radical expressions

  • 1) Isolate radical on one side of the equation
  • 2) Square both sides of the equation to eliminate radical
  • 3) Simplify and solve as you would any equations
  • 4) Substitute answers back into original equation to make sure that your solutions are valid (there could be some extraneous roots that do not satisfy the original equation and that you must throw out)

Video of How to Solve Radical Equations

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Practice Problems

Problem 1

Solve the radical Equation Below

Follow the steps for solving radical equations

Step 1

Isolate the radical

Step 2

Square both sides

Step 3

Solve expression

x = 10
Step 4

Substitute answer into original radical equation to verify that the answer is a real number

Problem 2

Solve the radical Equation Below

Remember how to solve radical equations

Step 1

Isolate the radical

Step 2

Square both sides

Step 3

Solve expression

3x = 23
Step 4

Substitute answer into original radical equation to verify that the answer is a real number

Problem 3

Solve the following radical equation:
$$ \sqrt{3x -11} = 3x -x $$

Remember how to solve radical equations

Step 1

Isolate the radical

Step 2

Square both sides

Step 3

Solve expression

This quadratic equation can be solved by factoring
0 =(x -4)(x-5)
x = 4, x = 5

Step 4

Substitute answer into original radical equation to verify that the answer is a real number

$$ \sqrt{3x -11} = 3x -x \\ \sqrt{3 (\color{Red}{4}) -11} = 3 \cdot (\color{Red}{4}) -\color{Red}{4} \\ \sqrt{1} = 8 \\ 1 \color{red}{ \ne } 8 $$

Therefore, reject 4 as a solution, check 5

$$ \sqrt{3x -11} = 3x -x \\ \sqrt{3 (\color{Red}{5}) -11} = 3(\color{Red}{5}) - \color{Red}{5} \\ \sqrt{15 -11} = 15 - 5 \\ \sqrt{15 -11} = 15 - 5 \\ \sqrt{4} = 10 \\ 2 = 10 \\ \color{red}{ \ne } 10 $$

Therefore, reject 5 as a solution

Since both our solutions were rejected, there are no real solutions to this equation.


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