Operations with Radicals

Simplify  $\sqrt{80}$  as much as possible.

•  $2\sqrt{20}$  

•  $8\sqrt{10}$  

•  $4\sqrt{5}$  

• Cannot be simplified further

Simplify  $\sqrt{18x^4}$  as much as possible.

•  $x^2\sqrt{18}$  

•  $3\sqrt{2x}$  

•  $6\sqrt{x}$  

•  $3x^2\sqrt{2}$  

Select all of the following radicals that are in fully simplified form.

• $-2\sqrt{36}$

• $3\sqrt{22}$

• $\sqrt{35}$

• $3\sqrt{3}$

Multiply:  $2\sqrt{3}\cdot4\sqrt{27}$  

•  $72$  

•  $8\sqrt{30}$  

•  $6\sqrt{81}$  

•  $84$  

Divide:  $\frac{5\sqrt{12}}{15\sqrt{3}}$  

•  $\frac{100}{15}$  

•  $\frac{\sqrt{9}}{3}$  

•  $\frac{2}{3}$  

•  $\frac{4}{3}$  

Here's a "proof," using nothing but radicals, that  $-1\ =\ 1$ :

 $-1\ =\sqrt{-1}\cdot\sqrt{-1}\ =\ \sqrt{-1\cdot-1}$   
 $=\sqrt{1\ }=\ 1$  

Which step contains the mistake? Explain why. Consider the first equals sign to be the first step, the second equals sign to be the second step, and so on.

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Add:  $3\sqrt{7}\ -2\sqrt{28}+10\sqrt{4}$ 

•  $-\sqrt{7}+10\sqrt{4}$  

•  $-9\sqrt{11}$  

•  $20-\sqrt{7}$  

• Cannot simplify any further

Add: $6\sqrt{24}-24\sqrt{6}$  

•  $-12\sqrt{6}$  

•  $-18\sqrt{18}$  

•  $18\sqrt{6}$  

•  $12\sqrt{6}$  

Which number is larger: $30\sqrt{20}\$  or  $15\sqrt{80}$ ? 

•  $30\sqrt{20}$  

•  $15\sqrt{80}$  

• These numbers are equal

• There's no way to tell

• False

• Not true

• Preposterous!

• Nonsense

• *sobs uncontrollably*