HW: Rationalizing the Denominator

Rationalizing the denominator involves eliminating any irrational numbers (like square roots) from the denominator of a fraction.

Multiply both the numerator and denominator by $$\sqrt{b}$$ to get $$\frac{a\sqrt{b}}{b}$$ .

The result is $$\frac{\sqrt{15}}{6}$$ .

The simplified form is $$\frac{2\sqrt{6}}{3}$$ .

The result is $$10\sqrt{2}$$ .

The simplified form is $$\frac{\sqrt{10x}}{5}$$ .

Multiply the numerator and denominator by the conjugate of the denominator.

The conjugate is $$a - b$$ .

Rationalizing the denominator can simplify calculations and make expressions easier to work with.

The result is $$\frac{\sqrt{2}}{2}$$ .