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Adding and Subtracting Radicals and Square Roots

Adding and Subtracting Radicals and Square Roots

You can add "like" square roots in the same way that you add other kinds of numbers. "Like" square roots are terms that have the same radical parts.

Formula showing 2 times the square root of 3 plus 2 times the square root of 3 with arrows pointing to the square root parts as the radical parts

The terms above can be simplified as follows:

Formula showing 2 times the square root of 3 plus 2 times the square root of 3 equals (2 + 2) times the square root of 3 which equals 4 times the square root of 3

Expressions with unlike radicals can be simplified in some cases. Notice that the principal roots of 100 and 9 are square numbers.

Formula showing the square root of 100 plus the square root of 9 equals 10 plus 3 which equals 13 Formula showing 4 times the square root of 100 plus 3 times the square root of 9 equals 4 times 10 plus 3 times 3 which equals 49

Remember that without like terms there is a limit to how much you can simplify.

Formula showing 2 times the square root of 2 plus 2 times the square root of 2 plus the square root of 3 equals 4 times the square root of 2 plus the square root of 3 \sqrt{12} + \sqrt{3} = \sqrt{4 \times 3} + \sqrt{3}