ALG Unit 5a: Rationalizing the 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.HSN.RN.A.1

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

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 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

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

•  $\frac{2\sqrt{30}}{3}$  

•  $10\sqrt{2}$  

• 20

•  $2\sqrt{10}$  

Tags

CCSS.HSN.RN.A.2

Simplify:
 $\frac{16\sqrt{42}}{2\sqrt{14}}$  

•  $8\sqrt{14}$  

•  $3\sqrt{8}$  

•  $8\sqrt{3}$  

•  $\frac{\sqrt{3}}{8}$  

Tags

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2