Answer:
[tex](4\sqrt{3}+6)[/tex]
Step-by-step explanation:
Simplify the radical part on by one
[tex]\frac{8\sqrt{6mn}+6\sqrt{8mn}}{2\sqrt{2mn}}[/tex]
square root (6) = sqrt(3) * sqrt(2)
square root (8) =sqrt(4)* sqrt(2)= 2sqrt(2)
so given expression becomes
[tex]\frac{8\sqrt{3}\sqrt{2}\sqrt{mn}+6*2\sqrt{2}\sqrt{mn}}{2\sqrt{2mn}}[/tex]
[tex]\frac{8\sqrt{3}\sqrt{2mn}+6*2\sqrt{2mn}}{2\sqrt{2mn}}[/tex]
[tex]\frac{8\sqrt{3}\sqrt{2mn}+12\sqrt{2mn}}{2\sqrt{2mn}}[/tex]
LEts factor out 2 sqrt(2mn) from the top
[tex]\frac{2\sqrt{2mn}(4\sqrt{3}+6)}{2\sqrt{2mn}}[/tex]
We cancel out 2sqrt(2mn) at the top and bottom
[tex](4\sqrt{3}+6)[/tex]
