Final answer:
To simplify the expression sqrt(5)(8 + 3 sqrt(6)), distribute the square root of 5 to both terms in the parentheses, and then simplify the resulting expression.
Step-by-step explanation:
To simplify the expression sqrt(5)(8 + 3 sqrt(6)), you can distribute the square root of 5 to both terms in the parentheses:
= sqrt(5)(8) + sqrt(5)(3 sqrt(6))
= 8 sqrt(5) + 3 sqrt(5) sqrt(6)
Next, simplify the second term using the property of square roots that allows multiplying under the square root:
= 8 sqrt(5) + 3 sqrt(30)
The simplified expression is 8 sqrt(5) + 3 sqrt(30). Therefore, option A. 8 sqrt(5) + 3 sqrt(30) is the correct choice.