﻿ How to solve radical equations. Video Tutorial and Step by step lesson

# 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)

### Practice Problems

Step 1

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

Step 1

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

Step 1

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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