Questions: sqrt(3)(sqrt(5)+12) sqrt(square)

Solution Steps

To simplify the expression \(\sqrt{3}(\sqrt{5}+12)\), we need to distribute \(\sqrt{3}\) across the terms inside the parentheses. This involves multiplying \(\sqrt{3}\) by \(\sqrt{5}\) and \(\sqrt{3}\) by 12. After performing these multiplications, we simplify the resulting expression by combining any like terms or simplifying any square roots if possible.

We start with the expression: \[ \sqrt{3}(\sqrt{5} + 12) \] We distribute \(\sqrt{3}\) across the terms inside the parentheses: \[ \sqrt{3} \cdot \sqrt{5} + \sqrt{3} \cdot 12 \]

Next, we simplify each term:

1. The first term becomes: \[ \sqrt{3} \cdot \sqrt{5} = \sqrt{15} \]
2. The second term simplifies to: \[ \sqrt{3} \cdot 12 = 12\sqrt{3} \]

Combining these results, we have: \[ \sqrt{15} + 12\sqrt{3} \]

The expression \(\sqrt{15} + 12\sqrt{3}\) cannot be simplified further, as there are no like terms to combine.

Final Answer