# Chapter 10 - Radical Expressions and Equations - 10-2 Simplifying Radicals - Practice and Problem-Solving Exercises - Page 610: 47

$\frac{4}{s}$

#### Work Step by Step

$\frac{8 \sqrt 7s}{2 \sqrt 7s^{3}}$ We simplify the constants $8 \div 2 = 4$ $\frac{4 \sqrt 7s}{\sqrt 7s^{3}}$ To simplify this, we cannot have a radical in the denominator. We multiply $\frac{4 \sqrt 7s}{\sqrt 7s^{3}}$ by $\frac{ \sqrt 7s^{3}}{\sqrt 7s^{3}}$ $\frac{4 \sqrt 7s}{\sqrt 7s^{3}} \times \frac{ \sqrt 7s^{3}}{\sqrt 7s^{3}}$ $\frac{4 \sqrt 49s^{4}}{ \sqrt (7s^{3})^{2}}$ Square root of $(7s^{3})^{2}$ is $7s^{3}$ because $7s^{3}$ x $7s^{3}$ = $(7s^{3})^{2}$ $\frac{4 \sqrt 49s^{4}}{7s^{3}}$ The square root of $49s^{4}$ is $7s^{2}$ because $7s^{2}$ x $7s^{2}$ = $49s^{4}$ $\frac{4 \times 7s^{2}}{7s^{3}}$ $7s^{2} \div 7s^{3} = s$ $\frac{4}{s}$

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