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:  $\frac{5\sqrt{12}}{15\sqrt{3}}$  

•  $\frac{100}{15}$  

•  $\frac{\sqrt{9}}{3}$  

•  $\frac{2}{3}$  

•  $\frac{4}{3}$  

Tags

CCSS.HSN.RN.A.2

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.

Tags

CCSS.HSN.RN.B.3

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

Tags

CCSS.6.NS.C.7A

CCSS.6.NS.C.7B

• False

• Not true

• Preposterous!

• Nonsense

• *sobs uncontrollably*