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Radical Expressions and Equations

Combine your skills of working with exponents and manipulating expressions for radical glory.

Rationalizing Denominators

         

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

\[ \frac1b \sqrt{\frac{b}{a}} - \frac3a \sqrt{\frac{a}{b}}. \]

Simplify \[\frac{\sqrt{7}}{\sqrt{7}+\sqrt{6}}+7+\sqrt{42}.\]

Simplify

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

Evaluate the above expression.

Simplify \(\frac{12+\sqrt{17}}{12-\sqrt{17}} = \frac{a}{c} + \frac{b}{c}\sqrt{17}\).

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