Rationalizing the Denominator

Rationalizing the denominator means to eliminate any irrational numbers (like square roots) from the denominator of a fraction.

The result is $$\frac{\text{a} \times \text{c}}{\text{b} \times \text{d}}$$ .

Multiply the numerator and denominator by $$\text{sqrt}(c)$$ to rationalize: $$\frac{\text{a} \times \text{sqrt}(c)}{c}$$ .

The simplified form is $$15\text{sqrt}(2)$$ .

The first step is to simplify each radical: $$\text{sqrt}(80) = 4\text{sqrt}(5)$$ and $$\text{sqrt}(20) = 2\text{sqrt}(5)$$ .

The rationalized form is $$\frac{\text{sqrt}(15)}{6}$$ .

The result is $$\text{sqrt}(a \times b)$$ .

Multiply the numerator and denominator by $$\text{sqrt}(3)$$ to get $$\frac{\text{sqrt}(3)}{3}$$ .

The simplified form is $$5\text{sqrt}(2)$$ .

The simplified form is $$a$$ , assuming $$a$$ is non-negative.