Radicals & surds

A square root asks for the non-negative number that, when multiplied by itself, gives the value inside the radical. To simplify $\sqrt{n}$, factor $n$ into a perfect square times the remaining factor, then pull the square root of the perfect square outside. For example, $\sqrt{12}=\sqrt{4\cdot 3}=2\sqrt{3}$. Radicals multiply together: $\sqrt{a}\sqrt{b}=\sqrt{ab}$. For variables, split even powers into squares: $\sqrt{x^4}=x^2$, while $\sqrt{x^3}=\sqrt{x^2\cdot x}=x\sqrt{x}$. Always simplify inside a radical before adding or subtracting separate radicals.