[tex] \frac{ 8\sqrt{6mn} + 6\sqrt{8mn} }{ 2\sqrt{2mn}}[/tex]
First, break it up into two fractions:
[tex]\frac{ 8\sqrt{6mn} + 6\sqrt{8mn} }{ 2\sqrt{2mn}} = \frac{8\sqrt{6mn}}{ 2\sqrt{2mn}} + \frac{6\sqrt{8mn}}{ 2\sqrt{2mn}} [/tex]
Next, you can simplify the numbers outside of the square root:
[tex]\frac{8\sqrt{6mn}}{ 2\sqrt{2mn}} + \frac{6\sqrt{8mn}}{ 2\sqrt{2mn}} = \frac{4\sqrt{6mn}}{\sqrt{2mn}} + \frac{3\sqrt{8mn}}{\sqrt{2mn}} [/tex]
Since the values are being acted by the same function, being under a radical, you can simplify these too:
[tex]\frac{4\sqrt{6mn}}{\sqrt{2mn}} + \frac{3\sqrt{8mn}}{\sqrt{2mn}} = {4\sqrt{3}} + {3\sqrt{4}}[/tex]
Finally, the square root of 4 is 2, so it would be expressed like this:
[tex] {4\sqrt{3}} + {3\sqrt{4}} = {4\sqrt{3}} + {3(2) = {4\sqrt{3}} + 6[/tex]
Your answer should be A.
