Radical Arithmetic: Now that we know how to work with radicals ($+$,$-$,$\times$,$\div$), we reap the reward of getting to solve radical equations.
A Prototype Example: $\sqrt{r-3}=5$
More Examples
$\sqrt{6 \gamma+2}-9=3$
$\sqrt{z-2}+9=7$
$\sqrt[3]{6 \eta-2}-4=3$
Process for Solving Radical Equations
1) Isolate radical on one side of the equation.
2) Raise both sides to a power equal to the index.
3) Simplify.
4) If no more radicals remain, solve the equation. Otherwise go back to step 1).
5) Check for extraneous (fake) solutions.
A Bountiful Bevy of Examples
$\sqrt[5]{h}=3$ (1 solution)
$\sqrt{ 7 \mu + 4}= \mu+2$ (2 solutions)
$\sqrt{ \xi^2+\xi+7}-\xi=9$ (1 solution)
$\sqrt{ 11 t + 2}= \sqrt{ 3 t + 7}$ (1 solution)
$\sqrt{ 3 \omega + 5}+2=3 \omega$ (1 solution)
Application: Calculating distance in the plane.
Example: Calculate the distance between the points $(-3,1)$ and $(5,-1)$.
Application: A pipe cleaning firm contracted to clean a pipe buried in a lake. Access points to the pipe are at points A and B on the edge of the lake, as shown in the figure.
