# How to Solve Radical Equations

An equation that contains a radical expression is called a radical equation, and in this blog post, we will teach you how to solve this type of equations.

## A step-by-step guide to solving Radical Equations

• Isolate the radical on one side of the equation.
• Square both sides of the equation to remove the radical.
• Solve the equation for the variable.
• Plugin the answer (answers) into the original equation to avoid extraneous values.

## Examples

### Radical Equations – Example 1:

Solve $$\sqrt{x}-5=15$$

Solution:

Add 5 to both sides: $$\sqrt{x}=20$$, Square both sides: $$(\sqrt{x})^2=20^2→x=400$$ Plugin the value of 400 for $$x$$ in the original equation and check the answer: $$x=400→\sqrt{x}-5=\sqrt{400}-5=20-5=15$$, So, the value of 400 for $$x$$ is correct.

### Radical Equations – Example 2:

What is the value of $$x$$ in this equation? $$2\sqrt{x+1}=4$$

Solution:

Divide both sides by 2. Then: $$2\sqrt{x+1}=4→\frac{2\sqrt{x+1}}{2}=\frac{4}{2}→\sqrt{x+1}=2$$ Square both sides: $$(\sqrt{(x+1)})^2=2^2$$, Then $$x+1=4→x=3$$
Substitute $$x$$ by 3 in the original equation and check the answer:
$$x=3→2\sqrt{x+1}=2\sqrt{3+1}=2\sqrt{4}=2(2)=4$$
So, the value of 3 for $$x$$ is correct.

### Radical Equations – Example 3:

Solve $$\sqrt{x}-8=-3$$

Solution:

Add 8 to both sides: $$\sqrt{x}=5$$
Square both sides: $$(\sqrt{x})^2=5^2→x=25$$
Substitute $$x$$ by 25 in the original equation and check the answer:
$$x=25→\sqrt{x}-8=\sqrt{25}-8=-3$$
So, the value of 25 for $$x$$ is correct.

### Radical Equations – Example 4:

What is the value of $$x$$ in this equation? $$4\sqrt{x+3}=40$$

Solution:

Divide both sides by 4. Then: $$4\sqrt{x+3}=40→\frac{4\sqrt{x+3}}{4}=\frac{40}{4}→\sqrt{x+3}=10$$ Square both sides: $$(\sqrt{(x+3)})^2=10^2$$, Then $$x+3=100→x=97$$
Substitute $$x$$ by 97 in the original equation and check the answer:
$$x=97→4\sqrt{x+3}=4\sqrt{97+3}=4\sqrt{100}=4(10)=40$$
So, the value of 97 for $$x$$ is correct.

1. $$\color{blue}{\sqrt{x}+6=8}$$
2. $$\color{blue}{\sqrt{x}-7=4}$$
3. $$\color{blue}{\sqrt{x+2}=10}$$
4. $$\color{blue}{2\sqrt{x-9}=14}$$
5. $$\color{blue}{\sqrt{2x-5}=\sqrt{x-1}}$$
6. $$\color{blue}{\sqrt{x+8}=\sqrt{2x+1}}$$
1. $$\color{blue}{x=4}$$
2. $$\color{blue}{x=121}$$
3. $$\color{blue}{x=98}$$
4. $$\color{blue}{x=58}$$
5. $$\color{blue}{x=4}$$
6. $$\color{blue}{x=7}$$

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