Radical Equations

Recall that the results obtained from squaring two equivalent expressions are equal:

1. If $\displaystyle a=b$, then $a^{2}=b^{2}$.

This is the important rule for solving radical equations. NOTE: If $a^{2}=b^{2}$, it is not necessarily true that $a=b$. For example $(-1)^{2}=(1)^{2}$, but $-1 \neq 1$. For this reason, we must check for extraneous solutions when working with radical equations.
To solve a radical equation containing one square root:

1. Isolate the square root expression on one side of the equal sign.
2. Square both sides of the equation.
3. Solve the resulting equation.
4. Check for extraneous solutions by making a substitution into the original equation to determine if your possible solutions are valid.

To solve a radical equation containing two square roots:

1. Isolate one square root expression on one side of the equal sign.
2. Square both sides of the equation. You should now have one radical left.
3. Isolate the second square root on one side of the equation.
4. Square both sides of the equation.
5. Solve the resulting equation.
6. Check for extraneous solutions by making a substitution into the original equation to determine if your possible solutions are valid.