Rationalizing the Denominator using Conjugates

What should you multiply $\frac{6}{1-\sqrt{5}}$  by to rationalize the denominator?

• -4

•  $1-\sqrt{5}$  

•  $1+\sqrt{5}$  

•  $-\frac{\left(3-3\sqrt{5}\right)}{2}$  

Tags

CCSS.HSN.RN.A.2

CCSS.HSA.APR.D.7

CCSS.HSA.APR.D.6

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.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.HSN.RN.A.2

CCSS.HSA.APR.D.7

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.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.HSN.RN.A.2

Rationalize the denominator:  $\frac{18}{-4-\sqrt{3}}$  

•  $\frac{54\sqrt{3}}{-19}$  

•  $\frac{-54\sqrt{3}}{13}$  

•  $\frac{-72+18\sqrt{3}}{13}$  

•  $\frac{-72+18\sqrt{3}}{19}$  

Tags

CCSS.HSN.RN.A.2

Rationalize the Denominator:
 $\frac{4}{3-\sqrt{2}}$  

•  $\frac{12+4\sqrt{2}}{7}$  

•  $\frac{3+\sqrt{2}}{4}$  

•  $\frac{12-2\sqrt{2}}{3}$  

•  $\frac{4-12\sqrt{2}}{7}$  

Tags

CCSS.HSN.RN.A.2

Rationalize the Denominator:

 $\frac{3}{3-\sqrt{3}}$  

•  $\frac{3+\sqrt{3}}{3}$  

•  $2+\sqrt{2}$  

•  $\frac{3+\sqrt{3}}{2}$  

•  $3+\sqrt{3}$  

Tags

CCSS.HSN.RN.A.2

Rationalize the Denominator:

 $\frac{\sqrt{3}}{2+4\sqrt{3}}$  

•  $\frac{\sqrt{3}+6}{22}$  

•  $22+\sqrt{3}$  

•  $6+\sqrt{22}$  

•  $\frac{-\sqrt{3}+6}{22}$  

Tags

CCSS.HSN.RN.A.2