Adding and Subtracting Radicals

Addition and Subtraction of Radicals

Learn to add, subtract and multiply radicals

Addition and Subtraction of Radicals

• Radicals can be added or subtracted only if they are like radicals.

• Like radicals are those having the same index or order.

•  $Example:$   $-3\sqrt{2\ }\ and\ 5\ \sqrt{2}$  

• If the radicals are unlike, we need to simplify.

Multiple Choice

Which one is needed to add or subtract radicals?

• Same index and same radicand

• Different index , same radicand

• Like radicands

• Unlike Radicands

Multiple Choice

Which of the following can be added or subtracted?

• $$2\sqrt{5}-3\sqrt{2}$$

• $$3\sqrt{2}+2\sqrt{3}$$

• $$2\sqrt{2}-\sqrt{2}$$

• $$\sqrt{3}-5\sqrt{5}$$

Multiple Choice

What shall we do if the radicals are unlike?

• Simplify if possible

• Do nothing

• Answer directly

• None of the above

How to add and subtract radicals

(Like Radicals)

• Add the coefficients.

• Simplify

•  $Example\ :\ 4\sqrt{2}+2\sqrt{2}-\sqrt{2}$  

•  $\left(4+2-1\right)\sqrt{2}\ \ \ \ \$  

•  $5\sqrt{2}$  

How to add and subtract radicals

(Unlike Radicals)

• Factor out to find a perfect root.

• Simplify then operate.

• Example of Factorization with Perfect root

•  $2\sqrt{8}=2\sqrt{\left(4\right)\left(2\right)}=2\left(\sqrt{4}\right)\left(\sqrt{2}\right)=2\left(2\right)\left(\sqrt{2}\right)=4\sqrt{2}$  

•  $5\sqrt{48}=5\ \sqrt{\left(16\right)\left(3\right)}=5\left(\sqrt{16}\right)\left(\sqrt{3}\right)=5\left(4\right)\left(\sqrt{3}\right)=20\sqrt{3}$  

How to add or subtract (unlike radicals)

•  $5\sqrt{50}+3\sqrt{8}-8\sqrt{32}$                                 Factor out perfect roots.

•  $5\sqrt{\left(25\right)\left(2\right)}+3\sqrt{\left(4\right)\left(2\right)}-8\sqrt{\left(16\right)\left(2\right)}$   Simplify perfect roots and multiply to coefficient.

•  $5\left(5\right)\sqrt{2}+3\left(2\right)\sqrt{2}-8\left(4\right)\sqrt{2}$ 

•  $25\sqrt{2}+6\sqrt{2}-24\sqrt{2}$                                  Operate 

•  $\left(25+6-24\right)\sqrt{2}$                                         Simplify

•  $7\sqrt{2}$  

Multiple Choice

$$Operate\ the\ radicals\ 2\sqrt{3}+3\sqrt{3}$$  

• $$5\sqrt{6}$$  

• $$5\sqrt{9}$$  

• $$5\sqrt{3}$$  

• $$5$$  

Multiple Choice

$$Operate\ the\ radicals\ 8\sqrt{5}-2\sqrt{5}$$  

• $$6\sqrt{5}$$  

• $$6$$  

• $$6\sqrt{10}$$  

• $$6\sqrt{0}$$

Poll

How do you feel today?

Multiple Choice

Operate this $$3\sqrt{12}+4\sqrt{8}-3\sqrt{27}$$

• $$8\sqrt{2}-3\sqrt{3}$$  

• $$5\sqrt{5}$$  

• $$4\sqrt{-7}$$  

• $$-3\sqrt{2}+8\sqrt{2}$$