# Solve for: 6sqrt((7)/(5))-2sqrt((5)/(7))-3sqrt(140)

## Expression: $6\sqrt{ \frac{ 7 }{ 5 } }-2\sqrt{ \frac{ 5 }{ 7 } }-3\sqrt{ 140 }$

To take a root of a fraction, take the root of the numerator and denominator separately

$6 \times \frac{ \sqrt{ 7 } }{ \sqrt{ 5 } }-2\sqrt{ \frac{ 5 }{ 7 } }-3\sqrt{ 140 }$

To take a root of a fraction, take the root of the numerator and denominator separately

$6 \times \frac{ \sqrt{ 7 } }{ \sqrt{ 5 } }-2 \times \frac{ \sqrt{ 5 } }{ \sqrt{ 7 } }-3\sqrt{ 140 }$

$6 \times \frac{ \sqrt{ 7 } }{ \sqrt{ 5 } }-2 \times \frac{ \sqrt{ 5 } }{ \sqrt{ 7 } }-6\sqrt{ 35 }$

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*}

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