Practice Radical Operations in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Adding, subtracting, and multiplying expressions that contain radicals. Like terms (same radicand) can be combined for addition and subtraction; for multiplication, use \sqrt{a} \cdot \sqrt{b} = \sqrt{ab}.
Treat simplified radicals like variables: 3\sqrt{5} + 2\sqrt{5} = 5\sqrt{5} works just like 3x + 2x = 5x. You can only combine radicals with the SAME radicand. Multiplication is more flexible since \sqrt{a} \cdot \sqrt{b} = \sqrt{ab} always works.
Example 1
easySimplify 3\sqrt{5} + 7\sqrt{5}.
Example 2
mediumSimplify \sqrt{12} + \sqrt{27}.
Example 3
mediumMultiply \sqrt{6} \cdot \sqrt{10} and simplify.
Example 4
hardExpand and simplify (\sqrt{3} + \sqrt{2})(\sqrt{3} - \sqrt{2}).