# What is a radical expression?

A radical expression is a numerical expression or an algebraic expression that include a radical.

See below 2 examples of radical expressions.

$$\sqrt{x^2 + 5} \ and \ 10\sqrt[5]{32}$$

A radical expression can also have fractions

$$\sqrt{\frac{32} {6}} \ and\ \sqrt{\frac{3s^3}{27s}}$$

There are 3 important pieces in any radical expressions. These are the radical sign, the radicand, and the index.

$$in\ 10\sqrt[5]{32},$$

$$The \ symbol\ \sqrt{ } is \ called \ a\ radical\ sign$$
The expression within the radical sign is called a radicand. In this case, the radicand is 32.

The number 5 is called the index.

An index of 5 means that we are looking for the fifth root. An index of 3 means that we are looking for the cube root.

An index of 2 is the square root. Usually, when the index is 2, we do not show the 2.

$$nth\ root\ of\ a \ = \sqrt[n]{a},$$

If the index n is even, the radicand a must be nonnegative for the root to be a real number.

For example, the following radical expressions do not have a real number root.

$$\sqrt[4]{-16} \ and\ \sqrt{-4}$$

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