8.5 Rationalizing Denominator

Rationalize the denominator:
 $\frac{\sqrt{5}}{2\sqrt{3}}$  

•  $\frac{\sqrt{15}}{6}$  

•  $\frac{\sqrt{15}}{18}$  

•  $\frac{5\sqrt{3}}{6}$  

•  $\frac{5\sqrt{3}}{18}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

Rationalize the denominator:
 $\frac{2\sqrt{8}}{\sqrt{12}}$  

•  $\frac{\sqrt{96}}{6}$  

•  $\frac{2\sqrt{6}}{3}$  

•  $\frac{2\sqrt{96}}{12}$  

•  $\frac{4\sqrt{2}}{2\sqrt{3}}$  

Tags

CCSS.HSN.RN.A.2

Divide:
 $\frac{10\sqrt{30}}{\sqrt{15}}$  

•  $\frac{2\sqrt{30}}{3}$  

•  $10\sqrt{2}$  

• 20

•  $2\sqrt{10}$  

Tags

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2

What is the conjugate of:
 $8+3\sqrt{6}$  

•  $8+3\sqrt{6}$  

•  $3\sqrt{6}-8$  

•  $8-3\sqrt{6}$  

•  $3\sqrt{6}+8$  

Tags

CCSS.HSN.CN.A.3

What should you multiply $\frac{3\sqrt{2}}{2-\sqrt{7}}$  by to rationalize the denominator?

•  $2-\sqrt{7}$  

•  $\sqrt{7}$  

•  $2+\sqrt{7}$  

•  $\sqrt{2}$  

Tags

CCSS.HSA.APR.D.7

CCSS.HSN.RN.A.2

 $\frac{-2}{1+\sqrt{6}}$  Rationalize the following:

•  $\frac{1+\sqrt{6}}{-2}$  

•  $\frac{-2+2\sqrt{6}}{-5}$  

•  $-\frac{2\sqrt{6}}{6}$  

•  $-2\sqrt{6}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSN.RN.A.2

Rationalize the following: $\frac{\sqrt{2}}{\sqrt{3}+\sqrt{5}}$  

•  $\frac{\sqrt{6}-\sqrt{10}}{8}$  

•  $\frac{\sqrt{6}-\sqrt{10}}{-2}$  

•  $\frac{\sqrt{6}+\sqrt{10}}{8}$  

•  $\frac{2\sqrt{3}+2\sqrt{5}}{-2}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSN.RN.A.2

 $\frac{3+5\sqrt{3}}{4-2\sqrt{3}}$  Rationalize:

•  $\frac{-9+7\sqrt{3}}{2}$  

•  $\frac{-18+14\sqrt{3}}{4}$  

•  $\frac{21+13\sqrt{3}}{2}$  

•  $\frac{24-26\sqrt{3}}{4}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

Simplify the radical

• 
• 
• 
• 

Tags

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2

Simplify: $\frac{\sqrt{12x^2}}{\sqrt{30x}}$  

•  $\sqrt{2x}$  

•  $2\sqrt{x}$  

•  $\frac{\sqrt{10x}}{5}$  

•  $\frac{\sqrt{5x^{ }}}{2}$