Simplify $\large \frac { \sqrt { 49x } }{ \sqrt { 21y } } \div \frac { \sqrt { 8z } }{ \sqrt { xyz } } \div \frac { \sqrt { 338x } }{ \sqrt { 18y } } $
Converting back to multiplication gives:
\(\quad \dfrac{\sqrt{49x}}{\sqrt{21y}} \div \dfrac{\sqrt{8z}}{\sqrt{xyz}} \div \dfrac{\sqrt{338x}}{\sqrt{18y}}\\ =\dfrac{\sqrt{49x}}{\sqrt{21y}} \times \dfrac{\sqrt{xyz}}{\sqrt{8z}} \times \dfrac{\sqrt{18y}}{\sqrt{338x}}\\ = \dfrac{21\sqrt 2 xy \sqrt z}{52 \sqrt{21}\sqrt{xyz}}\\ = \dfrac{\sqrt{42xy}}{52}\)