R.4 Dividing Radicals Practice

A radical is an expression that includes a root, such as a square root (√) or cube root (∛). For example, $$\frac{1}{\text{√}4}$$ is a radical.

To simplify $$\frac{4}{\text{√}6}$$ , multiply the numerator and denominator by $$\text{√}6$$ to get $$\frac{4\text{√}6}{6}$$ , which simplifies to $$\frac{2\text{√}6}{3}$$ .

Rationalizing the denominator involves eliminating any radicals in the denominator of a fraction by multiplying the numerator and denominator by a suitable radical.

$$\frac{3}{\text{√}3}$$ simplifies to $$\text{√}3$$ .

To divide radicals, you can simplify them as $$\frac{\text{√}5}{\text{√}10} = \text{√}\frac{5}{10} = \text{√}\frac{1}{2} = \frac{\text{√}2}{2}$$ .

$$\text{√}\frac{11}{22} = \frac{\text{√}11}{\text{√}22} = \frac{\text{√}11}{\text{√}(2 \times 11)} = \frac{\text{√}11}{\text{√}11 \times \text{√}2} = \frac{1}{\text{√}2} = \frac{\text{√}2}{2}$$ .

$$\frac{\text{√}15}{2\text{√}6} = \frac{\text{√}15}{\text{√}(4 \times 6)} = \frac{\text{√}15}{2\text{√}6} = \frac{\text{√{10}}}{4}$$ .

Simplifying a radical expression means to rewrite it in a simpler form, often by removing any perfect squares or cubes from under the radical sign.

Radicals can be expressed as exponents; for example, $$\text{√}x = x^{1/2}$$ and $$\text{∛}x = x^{1/3}$$ .

You can combine radicals only if they have the same radicand; for example, $$\text{√}2 + \text{√}2 = 2\text{√}2$$ .