Factor the number inside the square root into perfect-square factors
Rewrite the square root as the product of the square root of each factor
Replace square-rooted perfect squares with their simplified values
Combine like radicals if possible (same radicand)
Simplify expressions with variables by factoring out perfect-square variable factors (e.g., pull out squares like (x^2))
Use ( sqrt{a}sqrt{b}=sqrt{ab} ) to combine radicals when helpful
Use ( sqrt{a}/sqrt{b}=sqrt{a/b} ) to simplify quotients when helpful
Rationalize denominators when a radical remains in the denominator
Check that no perfect-square factors remain inside the radical
Keep radicals in simplest form with no common perfect-square factors outside
Example patterns to use:
( sqrt{n}=sqrt{(text{perfect square})cdot(text{remaining})}=text{outside factor}cdotsqrt{text{remaining}} )
( sqrt{50}= sqrt{25cdot 2}=5sqrt{2} )
( sqrt{72}= sqrt{36cdot 2}=6sqrt{2} )
( sqrt{12x^2}= sqrt{4cdot 3cdot x^2}=2xsqrt{3} )