Algebra

Radical Expressions and Equations

Rationalizing Denominators

         

Given that a>0 a>0 , b>0b>0, and ab=4 \sqrt{ab}=4 , evaluate

1bba3aab. \frac1b \sqrt{\frac{b}{a}} - \frac3a \sqrt{\frac{a}{b}}.

Simplify 77+6+7+42.\frac{\sqrt{7}}{\sqrt{7}+\sqrt{6}}+7+\sqrt{42}.

Simplify

12312343+23+1. \frac{1}{\sqrt[3]{2}-1} - \frac{\sqrt[3]{2}}{\sqrt[3]{4} + \sqrt[3]{2} + 1}.

Evaluate the above expression.

Simplify 12+171217=ac+bc17\frac{12+\sqrt{17}}{12-\sqrt{17}} = \frac{a}{c} + \frac{b}{c}\sqrt{17}.

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