Rationalizing Denominators

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.SSE.B.3

CCSS.HSN.RN.A.2

Rationalize the denominator:
 $\frac{7\sqrt{3}}{\sqrt{10}}$  

•  $\frac{70\sqrt{3}}{10}$  

•  $\frac{7\sqrt{3}}{100}$  

•  $\frac{7\sqrt{30}}{10}$  

•  $7\sqrt{3}$  

Tags

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

 $\frac{10+8\sqrt{7}}{\sqrt{31}}$  

•  $\frac{3\sqrt{221}}{16}$  

•  $\frac{8\sqrt{31}+11\sqrt{217}}{31}$  

•  $\frac{10\sqrt{31}+8\sqrt{217}}{31}$  

•  $\frac{10\sqrt{33}+8\sqrt{231}}{33}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSN.RN.A.2

Multiply:
 $\left(4+\sqrt{2}\right)\left(4-\sqrt{2}\right)$  

•  $16-\sqrt{2}$  

•  $4-\sqrt{2}$  

• 14

• 18

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

CCSS.HSN.RN.A.2

What is the conjugate of:
 $5+\sqrt{7}$  

• 18

•  $5+\sqrt{7}$  

•  $5-\sqrt{7}$  

• 32

Tags

CCSS.HSN.CN.A.3

What is the conjugate of:
 $-3\sqrt{2}-6$  

•  $-3\sqrt{2}+6$  

•  $3\sqrt{2}+6$  

•  $-6-3\sqrt{2}$  

•  $-2\sqrt{3}-6$  

Tags

CCSS.HSN.CN.A.3

CCSS.HSN.CN.B.5

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

CCSS.HSN.CN.B.5

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.HSA.APR.D.6

CCSS.HSA.APR.D.7

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.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.SSE.B.3

CCSS.HSN.RN.A.2