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  • 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: $\frac{x^2-9} {\sqrt{3} - \sqrt{x}}$
    $(x+3)(\sqrt{3}+\sqrt{x})$
    $-(x+3)(\sqrt{3} + \sqrt{x})$
    $(x+3)(\sqrt{x}-\sqrt{3})$

Basic operations

Rationalizing denominator

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