Radicals & Simplifying Radical Expression

A radical expression is an expression that includes a root, such as a square root, cube root, etc. For example, $$\frac{1}{\text{sqrt}(x)}$$ is a radical expression.

To simplify a radical expression means to rewrite it in a simpler form, removing any perfect square factors from the radicand and ensuring no radicals remain in the denominator.

The radicand is the number or expression inside the radical symbol. For example, in $$\text{sqrt}(x)$$ , $$x$$ is the radicand.

To rationalize the denominator, multiply the numerator and denominator by a suitable radical that will eliminate the radical in the denominator.

The simplified form is $$\frac{7\text{sqrt}(30)}{10}$$ .

It is not in simplified form because it has a radical in the denominator.

The first step is to multiply the numerator and denominator by $$\text{sqrt}(6)$$ to eliminate the radical in the denominator.

A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, and 16 are perfect squares.

A radical is in simplest form when there are no perfect square factors in the radicand and no radicals in the denominator.

A radical expression is simplified if the radicand has no perfect square factors other than 1 and there are no radicals in the denominator.