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• Tests on rationalizing denominator
• Rationalizing denominator with two or more terms

# Rationalizing denominator with two or more terms

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•  Question 1: 1 pts The conjugate of $2+\sqrt{2}$ is $2-\sqrt{2}$
•  Question 2: 1 pts The conjugate of $-\sqrt{a}-1$ is $\sqrt{a}+1$
•  Question 3: 1 pts To rationalize denominator in $\frac{1}{\sqrt{2}+1}$ we multiply both numerator and denominator with.
 $1+\sqrt{2}$ $1-\sqrt{2}$ $\sqrt{2}-1$
•  Question 4: 1 pts To rationalize denominator in $\frac{1}{\sqrt{3}-\sqrt{2}}$ we multiply both numerator and denominator with.
 $\sqrt{3}+\sqrt{2}$ $\sqrt{3}-\sqrt{2}$ $\sqrt{2}-\sqrt{3}$
•  Question 5: 1 pts Is the following equation true or false: $$\frac{1}{\sqrt{3}-\sqrt{2}} = \sqrt{3}+\sqrt{2}$$
•  Question 6: 2 pts Rationalize denominator $\frac{1}{2-\sqrt{3}}$
 $4+\sqrt{3}$ $4-\sqrt{3}$ $2+\sqrt{3}$
•  Question 7: 2 pts Rationalize denominator: $\frac{\sqrt{3} - \sqrt{2} } {\sqrt{3} + \sqrt{2}}$
 $5 + \sqrt{6}$ $5 - \sqrt{6}$ $5 + 2\sqrt{6}$ $5 - 2\sqrt{6}$
•  Question 8: 2 pts Rationalize denominator: $\frac{20} {\sqrt{20} - \sqrt{10}}$
 $\frac{20(\sqrt{20} +\sqrt{10})}{10}$ $2(\sqrt{20} +\sqrt{10})$ $2(\sqrt{20} - \sqrt{10})$
•  Question 9: 3 pts Is the following equation true or false: $$\frac{8+\sqrt{2}}{2-\sqrt{2}}=9+5\sqrt{2}$$
•  Question 10: 3 pts Is the following equation true or false: $$\frac{\sqrt{3}+\sqrt{4}}{\sqrt{2}-\sqrt{3}}=3+2\sqrt{2}+2\sqrt{3}+\sqrt{6}$$
•  Question 11: 3 pts Rationalize denominator: $\frac{\sqrt{a}} {\sqrt{a} + 1}$
 $\frac{a-\sqrt{a}}{a-1}$ $\frac{a-\sqrt{a}}{a+1}$ $\frac{a}{a-1}$ $\frac{\sqrt{a}}{a+1}$
•  Question 12: 3 pts Rationalize denominator: $\frac{x^2-9} {\sqrt{3} - \sqrt{x}}$
 $(x+3)(\sqrt{3}+\sqrt{x})$ $-(x+3)(\sqrt{3} + \sqrt{x})$ $(x+3)(\sqrt{x}-\sqrt{3})$