# 6. Equations With Radicals

It is important in this section to **check your solutions** in the original equation, as the process that we use to solve these
often produces solutions which actually don't work when subsituted back into the original equation.

(In fact, it is **always** good to check solutions for equations - you learn so much more about why things work the way they do. ^_^)

### Example

Solve** **`sqrt(2x+6)=2x`

### Exercises

**1. **Solve** **`sqrt(3x+4)=x`

**2.** Solve `sqrt(13+sqrtx)=sqrtx+1`

**3. **Solve `root(4)(x+10)=sqrt(x-2)`

**4. **In the study of spur gears in contact, the following
equation arises:

`kC=sqrt(R_1^2-R_2^2)+sqrt(r_1^2-r_2^2)-A`

Solve for `r_1^2`.

[Being able to solve equations like this is important for science and engineering. We often need to solve for a particular variable in a formula.]

### Search IntMath, blog and Forum

### Online Algebra Solver

This algebra solver can solve a wide range of math problems.

Go to: Online algebra solver

### Algebra Lessons on DVD

Easy to understand algebra lessons on DVD. See samples before you commit.

More info: Algebra videos

### The IntMath Newsletter

Sign up for the free **IntMath Newsletter**. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!