## Elementary Algebra

$\dfrac{\sqrt{37}}{3}$
Recall, we are not allowed to have radicals in the denominator of a fraction. Using the properties of radicals, the given expression, $\sqrt{4\dfrac{1}{9}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{\dfrac{37}{9}} \\\\= \dfrac{\sqrt{37}}{\sqrt{9}} \\\\= \dfrac{\sqrt{37}}{\sqrt{(3)^2}} \\\\= \dfrac{\sqrt{37}}{3} .\end{array}
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