How to Add and Subtract Square Roots

To add or subtract square roots, you need to simplify the radicals so that they have the same radicand (the number inside the radical symbol).

Here are the general steps for adding or subtracting square roots:

1. Identify the radicands of the square roots and check if they are the same.

2. If the radicands are the same, add or subtract the coefficients (the numbers in front of the square roots).

For example:

√12 + √3 = √(4 x 3) + √3 = 2√3 + √3 = 3√3

In this example, we first simplified √12 to 2√3 by factoring 12 into 4 and 3. Then we added 2√3 and √3 by combining their coefficients to get 3√3.

3. If the radicands are not the same, simplify them by factoring out the perfect squares.

For example:

√12 + √27 = √(4 x 3) + √(9 x 3) = 2√3 + 3√3 = 5√3

In this example, we simplified √12 to 2√3 and √27 to 3√3 by factoring out the perfect square 4 and 9, respectively. Then we added 2√3 and 3√3 by combining their coefficients to get 5√3.

Similarly, to subtract square roots, follow the same steps and then combine like terms.

For example:

√27 - √12 = √(9 x 3) - √(4 x 3) = 3√3 - 2√3 = √3

In this example, we simplified √27 to 3√3 and √12 to 2√3 by factoring out the perfect square 9 and 4, respectively. Then we subtracted 2√3 from 3√3 to get √3.