Operations with Radicals Worksheet with Answer Key

What's on the worksheet

1. Multiply the radicals and give each answer in simplest form.
   \sqrt{12}\cdot\sqrt{15}3\sqrt{14}\cdot 2\sqrt{21}\sqrt{5}\cdot\sqrt{10}\cdot\sqrt{8}-4\sqrt{3}\cdot 5\sqrt{27}\sqrt{15}\cdot\sqrt{35}\cdot\sqrt{3}
2. Divide the radicals and give each answer in simplest form.
   \dfrac{\sqrt{360}}{\sqrt{10}}\dfrac{18\sqrt{150}}{3\sqrt{3}}\sqrt{\dfrac{45}{16}}\dfrac{\sqrt{2}\cdot\sqrt{30}}{\sqrt{12}}\dfrac{\sqrt{80}}{\sqrt{125}}
3. Add or subtract radicals after simplifying each root.
   \sqrt{75} - \sqrt{12} + \sqrt{27}4\sqrt{18} - \sqrt{50} + 2\sqrt{3}\sqrt{44} + \sqrt{99} - 3\sqrt{11}\sqrt{8}\cdot\sqrt{3} + 5\sqrt{6} - \sqrt{54}
4. Expand and simplify products with radicals.
   2\sqrt{5}\left(\sqrt{10} - 3\sqrt{5}\right)\left(2 - \sqrt{7}\right)\left(5 + 3\sqrt{7}\right)\left(\sqrt{6} + \sqrt{2}\right)^2\left(2\sqrt{3} - 5\right)\left(2\sqrt{3} + 5\right)\left(\sqrt{5} + \sqrt{3}\right)\left(\sqrt{15} - 1\right)
5. Fill in each blank with the whole number that makes the statement true.
6. Lily's vegetable plot: find the exact area and perimeter from the side lengths.
7. Find what Jasmine did wrong squaring a sum with a radical, and find the correct value.