Rationalizing Denominators

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

• 18

•  $5+\sqrt{7}$  

•  $5-\sqrt{7}$  

• 32

Tags

CCSS.HSN.CN.A.3

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.1

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

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

•  $6+3\sqrt{2}$  

•  $3\sqrt{2}+6$  

•  $6-3\sqrt{2}$  

• 18

Tags

CCSS.HSN.CN.A.3

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.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

Rationalize the denominator:
 $\frac{7\sqrt{3}}{4\sqrt{7}}$  

•  $\frac{7\sqrt{21}}{28}$  

•  $\frac{7\sqrt{21}}{196}$  

•  $\frac{\sqrt{21}}{28}$  

•  $\frac{\sqrt{21}}{4}$  

Tags

CCSS.HSA.SSE.B.3

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

Rationalize the denominator:
 $\frac{1}{4\sqrt{10}}$  

•  $\frac{\sqrt{1}}{4}$  

•  $\frac{\sqrt{10}}{40}$  

•  $\frac{1}{4}$  

•  $\frac{\sqrt{10}}{400}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSN.RN.A.2

Rationalize the denominator:
 $\frac{\sqrt{4}}{\sqrt{121}}$  

•  $\frac{4}{11}$  

•  $\frac{\sqrt{484}}{121}$  

•  $\frac{2}{11}$  

•  $\frac{2\sqrt{121}}{121}$  

Tags

CCSS.HSN.RN.A.2

What is the conjugate of:
 $4\sqrt{2}-\sqrt{5}$  

•  $4\sqrt{2}+\sqrt{5}$  

•  $\sqrt{5}+4$  

•  $4\sqrt{2}-\sqrt{5}$  

• 27

Tags

CCSS.HSN.CN.A.3