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simplify (-7sqrt(85))/(6sqrt(85))

 Jul 8, 2015

Best Answer 

 #2
avatar+28125 
+10

It's probably simpler here just to cancel the √85 terms in the numerator and denominator, so that you are immediately left with -7/6.

.

 Jul 9, 2015
 #1
avatar+423 
+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...

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

.
 Jul 9, 2015
 #2
avatar+28125 
+10
Best Answer

It's probably simpler here just to cancel the √85 terms in the numerator and denominator, so that you are immediately left with -7/6.

.

Alan Jul 9, 2015

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