When the square root of a number is squared, the result is the original number. The reason why it’s called **square** root has to do with the area of the square that you obtain when graphing the radicand on the coordinate plane.

In general, the **principal square root** of a number $a$ is the nonnegative number that, when multiplied by itself, equals $a$. It is written as a **radical expression**, with a symbol called a **radical** over the term called the **radicand**: $\sqrt a$.

Again, radicals also have their rules that help you speed up calculations by hand.

The extension of the square root is the **nth root** which states that if $a$ is a real number with at least one nth root, then the **principal nth root** of $a$, written as $\sqrt[n] a$, is the number with the same sign as $a$ that, when raised to the nth power, equals $a$. The **index** of the radical is *n*.

Rational exponents are another way to express principal nth roots. The general form for converting between a radical expression with a radical symbol and one with a rational exponent is

$$a^\frac{m}{n} = (\sqrt[n] a)^m = \sqrt[n]{a^m}$$