Adding and Subtracting Higher Order Roots

(Videos) Adding and Subtracting Radicals

by mathman1024

Here's a video by mathman1024 going over the rules for adding and subtracting radicals.

In order to add/subtract radicals we must have like radicals. This means they have to have:

• same index
• same radicand $$3x+5x=8x\\ 3y^2+5y^2=8y^2\\ 3\sqrt2+5\sqrt2=8\sqrt2$$

Try these next ones on your own and then watch the video to see the answer!

1. $5\sqrt[3]{7}-12\sqrt[3]{7}$
2. $11\sqrt{2}+9\sqrt[3]{2}-5\sqrt{2}+4\sqrt[3]{2}$

In this video he looks at problems where you have to simplify the radials so that they have the same radical.

The first problem he looks at is: $\sqrt{8}+\sqrt{98}+\sqrt{32}$. As of right now we cannot add these together because they do not have the same radical. But these can be simplified, in which case they might have the same radical. $$\begin{align} &\sqrt{8}+\sqrt{98}+\sqrt{32}\\ &=\sqrt{4\cdot2}+\sqrt{49\cdot2}+\sqrt{16\cdot2}\\ &=2\sqrt2+7\sqrt2+4\sqrt2\\ &=13\sqrt2 \end{align}$$

Try this next one on your own and then watch the video to see the answer!

1. $\sqrt{90}+3\sqrt{160}$

Here are some more problems to solve. Try them then watch the videos to see the answers.

$5\sqrt{12}-8\sqrt{75}-2\sqrt{27}$

$-7\sqrt[3]{24}+3\sqrt[3]{-3000}$

$7\sqrt{200}-5\sqrt[3]{16}+8\sqrt[3]{432}-13\sqrt{72}+21\sqrt{722}$