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 equaitons
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
VIDEO

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Practice Problems
Problem 1) Solve the radical Equation Below :

Follow the steps for solving radical equations
1) Isolate the radical
2)Square both sides
3) Solve expression
x=10
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
1) Isolate the radical
2)Square both sides
3) Solve the equation
3x = 23

x=23/3

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
1) Isolate the radical
2)Square both sides
3) Solve the equation
This quadratic equation can be solved by factoring
0 =(x -4)(x-5)
x =4 , x = 5
4) Substitute answer into original radical equation to verify that the answer is a real number
Check 4
$$
\sqrt{3x -11} = 3x -x
\\
\sqrt{3 (\color{Red}{4}) -11} = 3 \cdot (\color{Red}{4}) -\color{Red}{4}
\\
\sqrt{1} = 8
\\
1 \color{red}{ \ne } 8
$$
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.