#1**+5 **

$${\frac{{\mathtt{\,-\,}}\left({\mathtt{7}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{85}}}}\right)}{\left({\mathtt{6}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{85}}}}\right)}}$$

Put the co-efficiencts into the surds by squaring them...

$${\frac{{\mathtt{\,-\,}}{\sqrt{{\mathtt{85}}{\mathtt{\,\times\,}}{\mathtt{49}}}}}{{\sqrt{{\mathtt{85}}{\mathtt{\,\times\,}}{\mathtt{36}}}}}}$$

Simplify...

$${\mathtt{\,-\,}}{\frac{{\sqrt{{\mathtt{4\,165}}}}}{{\sqrt{{\mathtt{3\,060}}}}}}$$

Which can be represented as:

$${\mathtt{\,-\,}}\left({\frac{{\mathtt{1}}}{{\sqrt{{\mathtt{3\,060}}}}}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{4\,165}}}}\right)$$

So we can put the surds together, again by squaring it:

$${\mathtt{\,-\,}}{\sqrt{{\mathtt{4\,165}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{1}}}{{{\sqrt{{\mathtt{3\,060}}}}}^{\,{\mathtt{2}}}}}\right)}}$$

Simplify...

$${\mathtt{\,-\,}}{\sqrt{{\frac{{\mathtt{4\,165}}}{{\mathtt{3\,060}}}}}}$$

Now we can simplfy the fraction:

$${\mathtt{\,-\,}}{\sqrt{{\frac{{\mathtt{833}}}{{\mathtt{612}}}}}}$$

And further...

$${\mathtt{\,-\,}}{\sqrt{{\frac{{\mathtt{49}}}{{\mathtt{36}}}}}}$$

.Sir-Emo-Chappington Jul 9, 2015