Final answer:
The expression (√5(8 + 3√6)) simplifies to 8√5 + 3√30 by distributing the square root of 5 across the terms inside the parentheses.
Step-by-step explanation:
To simplify the expression (√5(8 + 3√6)), we need to distribute the √5 across the terms within the parentheses.
First, multiply √5 by 8 to get 8√5. Next, multiply √5 by 3√6 to get 3√30 because when you multiply two square roots, you can multiply the numbers under the square roots together (5 * 6 = 30).
The simplified form of the expression is then 8√5 + 3√30, which matches option a).