Rationalizing Denominators

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

• 18

•  $5+\sqrt{7}$  

•  $5-\sqrt{7}$  

• 32

Tags

CCSS.HSN.CN.A.3

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

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

Rationalize the denominator:  $\frac{\sqrt{5}}{\sqrt{6}}$  

•  $\sqrt{5}$  

•  $\frac{\sqrt{30}}{6}$  

•  $\frac{\sqrt{5}}{6}$  

•  $\frac{\sqrt{30}}{36}$  

Tags

CCSS.HSN.RN.A.2

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

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

•  $\sqrt{2x}$  

•  $2\sqrt{x}$  

•  $\frac{\sqrt{10x}}{5}$  

•  $\frac{\sqrt{5x^{ }}}{2}$