# Chapter 7 - Section 7.4 - Adding and Subtracting Radical Expressions - 7.4 Exercises - Page 466: 45

$\dfrac{5\sqrt{5}}{6}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $\dfrac{2\sqrt{5}}{3}+\dfrac{\sqrt{5}}{6} ,$ change the terms to similar fractions by using the $LCD.$ $\bf{\text{Solution Details:}}$ To simplify the expression above, change the expressions to similar fractions (same denominator) by using the $LCD$. The $LCD$ of the denominators $3$ and $6$ is $6$ since it is the lowest number that can be exactly divided by the denominators. Multiplying the terms by an expression equal to $1$ that will make the denominator equal to the $LCD$ results to \begin{array}{l}\require{cancel} \dfrac{2\sqrt{5}}{3}\cdot\dfrac{2}{2}+\dfrac{\sqrt{5}}{6} \\\\= \dfrac{4\sqrt{5}}{6}+\dfrac{\sqrt{5}}{6} \\\\= \dfrac{(4+1)\sqrt{5}}{6} \\\\= \dfrac{5\sqrt{5}}{6} .\end{array}

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