Operations on Radicals

When adding and subtracting radical expressions, treat the radical like a variable whenever possible.

    \[\sqrt{a} + \sqrt{a} = 2\sqrt{a}\]

The roots need to be exactly the same (i.e. same index, same radicand) to be able to add or subtract.

Example 1: 5\sqrt{7} - 3 \sqrt{7} = 2\sqrt{7}


You got an idea of what it’s like to multiply roots when you learned to simplify radicals. The concept bridges over.

If two roots (with the same index) are multiplied, just multiply the inside numbers.

    \[\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\]

Example 2: \sqrt[5]{8} \cdot \sqrt[5]{4}=\sqrt[5]{32}      =2