To add and subtract radicals, add and subtract like radicals.

The distributive property is also used to add or subtract expressions with like radicals.

Simplification of the like radicals must be done before combining them.

 $\sqrt{45x}+3\sqrt{20x}-\sqrt{5x}=9\sqrt{5x}$  

The Product Law of Radicals is applied when multiplying radicals having the same indices.

 $\left(3-\sqrt{2}\right)\left(3+\sqrt{2}\right)$  are conjugates.

The product of two conjugates is the difference of two squares.

Rationalization is used in dividing radicals to avoid radicals as divisors.

If  $a=b$  , then  $a^2=b^2$  

A radical equation is an equation with a variable in the radicand.

 $8-x\sqrt{2}=5$  is a radical equation

An extraneous root or solution is an obtained value that does not satisfy the original equation.

 $\frac{9}{4}$  is a solution to  $5+2\sqrt{a}=2$  

 $4+\sqrt{y-2}=y$  has an extraneous root

 $\sqrt{m+5}=m+5$  has two roots

 $26$  is the solution to  $\sqrt{2x-3}=7$  

 $-3$  is the solution to  $2\sqrt{x^2+7}=2x-2$  

To solve   $\sqrt{2y+2}=\sqrt{3y-5}$  , you have to square both sides.