# 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.]

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