Pre-Calculus 11 Week 4 – Adding and Subtracting Square Roots

This week, we discussed adding and subtracting numbers with square roots, such as $2\sqrt{2} + 3\sqrt{2}$

The easiest way to learn how to add these numbers is simply looking at them the same way you would look at 2x + 3x in algebra. You can simplify this expression. 2x + 3x = 5x

But you wouldn’t be able to add, say, 2x + 2y together. The expression is already simplified. The same thing applies to roots!

You can add $2\sqrt{2} + 3\sqrt{2}$ together to make $5\sqrt{2}$ !

However, you are unable to simplify $4\sqrt{2} + 5\sqrt{3}$ , because the radicands aren’t the same.

If our square root is really big, like $\sqrt {128} + 3\sqrt{2}$ , we can still add them together! We just need to simplify the square root first. In this case, $\sqrt {128}$ simplifies into $8\sqrt {2}$ . Our steps are as follows: