6.2 Multiply and Divide Radicals

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

The square root of a number x is a value that, when multiplied by itself, gives x. It is denoted as $$\text{√}x$$ .

To multiply radical expressions, multiply the numbers outside the radicals and the numbers inside the radicals separately. For example, $$\text{√}a \times \text{√}b = \text{√}(ab)$$ .

Rationalizing the denominator involves eliminating any radicals from the denominator of a fraction. This is done by multiplying the numerator and denominator by a suitable radical.

The simplified form is $$\frac{\text{√}2}{2u}$$ .

The cube root of a number x is a value that, when multiplied by itself three times, gives x. It is denoted as $$\text{∛}x$$ .

To divide radical expressions, divide the numbers outside the radicals and the numbers inside the radicals separately. For example, $$\frac{\text{√}a}{\text{√}b} = \text{√}\frac{a}{b}$$ .

The simplified form is $$x^4$$ .

The product of radicals states that $$\text{√}a \times \text{√}b = \text{√}(ab)$$ .

The evaluated form is $$3p^3k^2\text{√}6k$$ .