# Chapter 10 - Radical Expressions and Equations - 10-2 Simplifying Radicals - Practice and Problem-Solving Exercises: 44

$\frac{3 \sqrt 10}{5}$

#### Work Step by Step

$\frac{3 \sqrt 6}{\sqrt 15}$ To simplify this, we cannot have a radical in the denominator. We multiply $\frac{3 \sqrt 6}{\sqrt 15}$ by $\frac{ \sqrt 15}{ \sqrt 15}$ $\frac{3 \sqrt 6}{\sqrt 15} \times \frac{ \sqrt 15}{ \sqrt 15}$ $\frac{3 \sqrt 90}{2 \sqrt 15^{2}}$ The factors of 90 is 9 x 10 $\frac{3 \sqrt 9 \sqrt 10}{\sqrt 15^{2}}$ Square root of 9 is 3 because 3 x 3 = 9 Square root of $15^{2}$ is 15 because 15 x 15 = $15^{2}$ $\frac{3 \times 3 \sqrt 10}{15}$ $\frac{9 \sqrt 10}{15}$ $9 \div 15$ can also be written as $3 \div 5$ $\frac{3 \sqrt 10}{5}$

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