To simplify the expression √5(8 + 3√6), we will follow a systematic approach that involves distributing the square root of 5 across the terms inside the parentheses.
1. **Distributing √5**: Start by distributing √5 to both terms in the parentheses:
√5 * 8 + √5 * 3√6
2. **Calculating Each Term**:
- The first term: √5 * 8 = 8√5
- The second term: √5 * 3√6 = 3√(5 * 6) = 3√30
3. **Combining the Terms**: Now, we can combine the results of both multiplications:
8√5 + 3√30
So the simplified expression for √5(8 + 3√6) is:
8√5 + 3√30
This final expression cannot be simplified further since the square roots of 5 and 30 do not have any common factors that could be simplified. Thus, the expression is in its simplest form!