Answer:
The answer is 4√3 - 6
Steps
(8√6mn + 6√8mn ) / 2√2mn
Factor out 2√mn from the expression
That's
2√mn × ( 4√6 - 3√8) / 2√2mn
Next reduce the fraction with 2
We have
√mn × ( 4√6 - 3√8) / √2mn
Factor √2 from the denominator
√mn × ( 4√6 - 3√8) / √2(√mn)
√mn will cancel each other
we get
( 4√6 - 3√8) / √2
Simplify the radical expression
That's
( 4√6 - 3× 2√2) / √2
= ( 4√6 - 6√2) / √2
Rationalize the surd
We get
( 4√6 - 6√2) / √2 × (√2 / √2)
= ( 4√6 - 6√2) (√2) / (√2)²
= 4√12 - 12 / 2
= (8 √3 - 12) / 2
Factor out 2 from the numerator
That's
2( 4 √ 3 - 6 ) /2
2 will cancel each other
so the final answer will be
4√3 - 6
Hope this helps you