Radicals and reasoning
Simplify a radical by pulling out the largest perfect square, and undo a radical equation by raising both sides to the matching power.
A worked example
√45 = √9 x √5 = 3√5. To solve √(x - 4) = 6, square both sides: x - 4 = 36, so x = 40.
The mistake people actually make
√8 + √32 is not √40. Simplify each radical first, then add the like terms to get 6√2. A single counterexample is enough to destroy a conjecture.