Question

Simplify. A) 4√3 + 6 B) 6√3 + 4 C) 6√6 + 3

Answer 1

$\frac{ 8\sqrt{6mn} + 6\sqrt{8mn} }{ 2\sqrt{2mn}}$

First, break it up into two fractions:

$\frac{ 8\sqrt{6mn} + 6\sqrt{8mn} }{ 2\sqrt{2mn}} = \frac{8\sqrt{6mn}}{ 2\sqrt{2mn}} + \frac{6\sqrt{8mn}}{ 2\sqrt{2mn}}$

Next, you can simplify the numbers outside of the square root:

$\frac{8\sqrt{6mn}}{ 2\sqrt{2mn}} + \frac{6\sqrt{8mn}}{ 2\sqrt{2mn}} = \frac{4\sqrt{6mn}}{\sqrt{2mn}} + \frac{3\sqrt{8mn}}{\sqrt{2mn}}$

Since the values are being acted by the same function, being under a radical, you can simplify these too:

$\frac{4\sqrt{6mn}}{\sqrt{2mn}} + \frac{3\sqrt{8mn}}{\sqrt{2mn}} = {4\sqrt{3}} + {3\sqrt{4}}$

Finally, the square root of 4 is 2, so it would be expressed like this:

${4\sqrt{3}} + {3\sqrt{4}} = {4\sqrt{3}} + {3(2) = {4\sqrt{3}} + 6$

Your answer should be A.