Rationalizing a Denominator Worksheet with Answer Key

What's on the worksheet

1. Rationalize each denominator and give the answer in simplest form.
   \dfrac{8}{\sqrt{6}}\dfrac{15}{2\sqrt{3}}\dfrac{\sqrt{5}}{\sqrt{8}}\dfrac{21}{\sqrt{12}}\dfrac{3\sqrt{2}}{\sqrt{20}}
2. Rationalize and simplify expressions with variables under the root.
   \dfrac{x}{\sqrt{3x}}\dfrac{10}{\sqrt{5y}}\sqrt{\dfrac{2}{x}}\dfrac{4x}{\sqrt{2x^3}}
3. Rationalize each denominator with the conjugate.
   \dfrac{6}{3 + \sqrt{3}}\dfrac{9}{\sqrt{7} - 2}\dfrac{3}{1 - \sqrt{5}}\dfrac{2}{\sqrt{11} + \sqrt{5}}\dfrac{\sqrt{5}}{\sqrt{10} + \sqrt{5}}
4. Write each expression as a single term in simplest form.
   \sqrt{3} + \dfrac{1}{\sqrt{3}}\sqrt{20} - \dfrac{10}{\sqrt{5}} + \sqrt{\dfrac{1}{5}}\dfrac{2}{\sqrt{6}} + \sqrt{\dfrac{3}{2}}\dfrac{1}{\sqrt{2} - 1} - \dfrac{1}{\sqrt{2} + 1}
5. Hannah's mosaic panel: find the width and another measurement from the length.
6. Find the error in Priya's rationalizing with a conjugate.
7. Rationalize three denominators and look for a pattern.