Questions: Multiply. √6(8+√5) Simplify your answer as much as possible. √

Solution Steps

To solve the given problem, we need to distribute the square root of 6 across the terms inside the parentheses. This involves multiplying the square root of 6 by 8 and then by the square root of 5. After performing these multiplications, we simplify the resulting expression if possible.

We start by distributing \(\sqrt{6}\) across the terms inside the parentheses: \[ \sqrt{6}(8 + \sqrt{5}) = \sqrt{6} \cdot 8 + \sqrt{6} \cdot \sqrt{5} \]

Next, we perform the multiplications: \[ \sqrt{6} \cdot 8 = 8\sqrt{6} \] \[ \sqrt{6} \cdot \sqrt{5} = \sqrt{30} \]

We combine the results from the multiplications: \[ 8\sqrt{6} + \sqrt{30} \]

Final Answer