5.) Rationalizing the Denominator

Please retry until you get 100% (If Quizizz errors on you and locks you out, give it a break for a while).

Favorite Fast Food?

• Panda Express

• Taco Bell

• McDonalds

• Subway

• Other

1.) Rationalize the denominator:
 $\frac{2\sqrt{8}}{\sqrt{12}}$  
Q1:  What should we multiply to the numerator and denominator?

•  $12$  

•  $\sqrt{12}$  

•  $\sqrt{8}$  

•  $2\sqrt{8}$  

To rationalize the denominator, we use the radical in the denominator and multiply it to the numerator and denominator.  So we will multiply by  $\sqrt{12}$ .

• K

• No u

1.) Rationalize the denominator:
 $\frac{2\sqrt{8}}{\sqrt{12}}$  
Q2:  What do we get after we multiply the numerator and denominator by  $\sqrt{12}$  ?

•  $\frac{2\sqrt{8}}{12}$  

•  $\frac{2\sqrt{96}}{12}$  

•  $\frac{24\sqrt{8}}{12}$  

•  $\frac{2\cdot8}{12}$  

Multiplying the numerator and denominator by  $\sqrt{12}$  , we get...
 $\frac{2\sqrt{8}}{\sqrt{12}}\ \cdot\ \frac{\sqrt{12}}{\sqrt{12}}\ =\ \frac{2\sqrt{8\cdot12}}{\sqrt{12\cdot12}}\ =\ \frac{2\sqrt{96}}{12}$  

• K

• No u

1.) Rationalize the denominator:
 $\frac{2\sqrt{8}}{\sqrt{12}}$  
Q3:  The above expression is equivalent to  $\frac{2\sqrt{96}}{12}$  .  Simplify the radical and numerator.

•  $\frac{8\sqrt{8}}{12}$  

•  $\frac{8\sqrt{6}}{12}$  

•  $\frac{12\sqrt{8}}{12}$  

•  $\frac{12\sqrt{6}}{12}$  

Tags

CCSS.HSN.RN.A.2

The  $\sqrt{96}$  simplifies into 
 $\sqrt{96}=\sqrt{2\times2\times2\times2\times2\times3}\ =\ 4\sqrt{6}$  .
So we get...
 $\ \frac{2\sqrt{96}}{12}\ =\ \frac{2\ \cdot4\sqrt{6}}{12}\ =\ \frac{8\sqrt{6}}{12}$  

• K

• No u

Tags

CCSS.HSN.RN.A.2

1.) Rationalize the denominator:
 $\frac{2\sqrt{8}}{\sqrt{12}}$  
Q4:  The above expression is equivalent to  $\frac{8\sqrt{6}}{12}$  .  Simplify the numerator and denominator.

•  $\frac{\sqrt{8}}{4}$  

•  $\frac{2\sqrt{6}}{3}$  

•  $\frac{8}{6}$  

•  $4$  

Tags

CCSS.HSN.RN.A.2

Values inside radicals do not interact will values outside radicals usually, so we can only work with the 8 and 12  in
 $\ \frac{8\sqrt{6}}{12}$  .
Simplifying fractions - we look for the largest number that goes into 8 and 12 (which is 4), and divide it out.  So we have
 $\ \frac{8\sqrt{6}}{12}\ =\ \frac{2\sqrt{6}}{3}$  

• K

• No u

Tags

CCSS.HSN.RN.A.2

1.) Rationalize the denominator:
 $\frac{7\sqrt{3}}{4\sqrt{7}}$  
Q1:  What should we multiply to the numerator and denominator?

•  $7$  

•  $\sqrt{7}$  

•  $\sqrt{3}$  

•  $7\sqrt{3}$  

•  $4\sqrt{7}$