# Chapter 10 - Section 10.5 - Rationalizing Numerators and Denominators of Radical Expressions - Exercise Set - Page 718: 61

$\sqrt{\dfrac{18x^{4}y^{6}}{3z}}=\dfrac{6x^{2}y^{3}}{\sqrt{6z}}$

#### Work Step by Step

$\sqrt{\dfrac{18x^{4}y^{6}}{3z}}$ Rewrite this expression as $\dfrac{\sqrt{9\cdot2(x^{4}y^6)}}{\sqrt{3z}}$ and simplify it: $\sqrt{\dfrac{18x^{4}y^{6}}{3z}}=\dfrac{\sqrt{9\cdot2(x^{4}y^6)}}{\sqrt{3z}}=\dfrac{3x^{2}y^{3}\sqrt{2}}{\sqrt{3z}}=...$ Multiply this fraction by $\dfrac{\sqrt{2}}{\sqrt{2}}$ and simplify again if possible: $...=\dfrac{3x^{2}y^{3}\sqrt{2}}{\sqrt{3z}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{3x^{2}y^{3}\sqrt{2^{2}}}{\sqrt{6z}}=\dfrac{3x^{2}y^{3}(2)}{\sqrt{6z}}=\dfrac{6x^{2}y^{3}}{\sqrt{6z}}$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.