Simplifying, Adding & Subtracting Radicals

Simplify:

 $2\sqrt{18}-\sqrt{27}-\sqrt{50}$  

•  $\sqrt{2}-3\sqrt{3}$   

•  $2\sqrt{-59}$  

•  $-2\sqrt{2}-3\sqrt{3}$  

•  $-3.782$  

Simplify:

 $\sqrt{18}\ -\ \ \sqrt{12}$  

•  $\sqrt{6}$  

•  $2\sqrt{3}$  

•  $3\sqrt{2}-\ 2\sqrt{3}$  

•  $\sqrt{-1}$  

Simplify:

 $\sqrt{5}+\sqrt{5}$  

•  $\sqrt{25}$  
  

•  $5$  
  

•  $2\sqrt{5}$  
  

•  $\sqrt{10}$  
  

The number under the radical symbol

is called the _____________.

• radical

• square root

• radicand

• index

Simplify:

 $\sqrt{300}+\sqrt{75}$ 

•  $15\sqrt{3}$  

•  $\sqrt{375}$  

•  $20\sqrt{5}$  

•  $16\sqrt{5}$  

When adding or subtracting square roots, what number HAS TO BE THE SAME?

• The coefficient (number in front of square root)

• The radicand (number in square root)

• The numbers don't matter

• Both have to be the same

Simplify:

 $\sqrt{20a^2b^4}$  

•  $2ab^2\sqrt{5}$  

•  $4ab^2\sqrt{5}$  

•  $5ab^2\sqrt{2}$  

•  $2a^2b^2\sqrt{5}$  

Simplify:

 $\sqrt{675}$  

•  $225\sqrt{3}$  

•  $15\sqrt{5}$  

•  $3\sqrt{15}$  

•  $15\sqrt{3}$  

Simplify:

 $\sqrt{x^7}$  

•  $x^3\sqrt{x}$  

•  $7x\sqrt{x^2}$  

•  $x^6\sqrt{x}$  

•  $\sqrt{x}$  

Simplify:

 $5\sqrt{117}$  

•  $15\sqrt{39}$  

•  $15\sqrt{13}$  

•  $45\sqrt{13}$  

•  $5\sqrt{117}$