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Tests on rationalizing denominator

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Current: Test on rationalizing denominator with two or more terms
  • Q1:
    1 pts
    The conjugate of $2+\sqrt{2}$ is $2-\sqrt{2}$
  • Q2:
    1 pts
    The conjugate of $-\sqrt{a}-1$ is $\sqrt{a}+1$
  • Q3:
    1 pts
    To rationalize denominator in $\frac{1}{\sqrt{2}+1}$ we multiply both numerator and denominator with.
    $1+\sqrt{2}$
    $1-\sqrt{2}$
    $\sqrt{2}-1$
  • Q4:
    1 pts
    To rationalize denominator in $\frac{1}{\sqrt{3}-\sqrt{2}}$ we multiply both numerator and denominator with.
    $\sqrt{3}+\sqrt{2}$
    $\sqrt{3}-\sqrt{2}$
    $\sqrt{2}-\sqrt{3}$
  • Q5:
    1 pts
    Is the following equation true or false: $$\frac{1}{\sqrt{3}-\sqrt{2}} = \sqrt{3}+\sqrt{2}$$
  • Q6:
    2 pts
    Rationalize denominator $\frac{1}{2-\sqrt{3}}$
    $4+\sqrt{3}$
    $4-\sqrt{3}$
    $2+\sqrt{3}$
  • Q7:
    2 pts
    Rationalize denominator: $\frac{\sqrt{3} - \sqrt{2} } {\sqrt{3} + \sqrt{2}}$
    $5 + \sqrt{6}$
    $5 - \sqrt{6}$
    $5 + 2\sqrt{6}$
    $5 - 2\sqrt{6}$
  • Q8:
    2 pts
    Rationalize denominator: $\frac{20} {\sqrt{20} - \sqrt{10}}$
    $\frac{20(\sqrt{20} +\sqrt{10})}{10}$
    $2(\sqrt{20} +\sqrt{10})$
    $2(\sqrt{20} - \sqrt{10})$
  • Q9:
    3 pts
    Is the following equation true or false: $$\frac{8+\sqrt{2}}{2-\sqrt{2}}=9+5\sqrt{2}$$
  • Q10:
    3 pts
    Is the following equation true or false: $$\frac{\sqrt{3}+\sqrt{4}}{\sqrt{2}-\sqrt{3}}=3+2\sqrt{2}+2\sqrt{3}+\sqrt{6}$$
  • Q11:
    3 pts
    Rationalize denominator: $\frac{\sqrt{a}} {\sqrt{a} + 1}$
    $\frac{a-\sqrt{a}}{a-1}$
    $\frac{a-\sqrt{a}}{a+1}$
    $\frac{a}{a-1}$
    $\frac{\sqrt{a}}{a+1}$
  • Q12:
    3 pts
    Rationalize denominator: $\frac{x^2-9} {\sqrt{3} - \sqrt{x}}$
    $(x+3)(\sqrt{3}+\sqrt{x})$
    $-(x+3)(\sqrt{3} + \sqrt{x})$
    $(x+3)(\sqrt{x}-\sqrt{3})$