$6 \times \frac{ \sqrt{ 7 } }{ \sqrt{ 5 } }-2\sqrt{ \frac{ 5 }{ 7 } }-3\sqrt{ 140 }$
To take a root of a fraction, take the root of the numerator and denominator separately$6 \times \frac{ \sqrt{ 7 } }{ \sqrt{ 5 } }-2 \times \frac{ \sqrt{ 5 } }{ \sqrt{ 7 } }-3\sqrt{ 140 }$
Simplify the radical expression$6 \times \frac{ \sqrt{ 7 } }{ \sqrt{ 5 } }-2 \times \frac{ \sqrt{ 5 } }{ \sqrt{ 7 } }-6\sqrt{ 35 }$
Calculate the product$\frac{ 6\sqrt{ 7 } }{ \sqrt{ 5 } }-2 \times \frac{ \sqrt{ 5 } }{ \sqrt{ 7 } }-6\sqrt{ 35 }$
Calculate the product$\frac{ 6\sqrt{ 7 } }{ \sqrt{ 5 } }-\frac{ 2\sqrt{ 5 } }{ \sqrt{ 7 } }-6\sqrt{ 35 }$
Rationalize the denominator$\frac{ 6\sqrt{ 35 } }{ 5 }-\frac{ 2\sqrt{ 5 } }{ \sqrt{ 7 } }-6\sqrt{ 35 }$
Rationalize the denominator$\frac{ 6\sqrt{ 35 } }{ 5 }-\frac{ 2\sqrt{ 35 } }{ 7 }-6\sqrt{ 35 }$
Calculate the difference$\begin{align*}&-\frac{ 178\sqrt{ 35 } }{ 35 } \\&\approx-30.08749\end{align*}$