Questions: Multiply. √3(√15-3√7) Simplify your answer as much as possible.

Solution Steps

To solve the expression \(\sqrt{3}(\sqrt{15} - 3\sqrt{7})\), we first distribute \(\sqrt{3}\) across the terms inside the parentheses:

\[ \sqrt{3} \cdot \sqrt{15} - \sqrt{3} \cdot 3\sqrt{7} \]

Simplify each term by multiplying the radicands:

1. \(\sqrt{3} \cdot \sqrt{15} = \sqrt{3 \times 15} = \sqrt{45}\)
2. \(\sqrt{3} \cdot 3\sqrt{7} = 3\sqrt{3 \times 7} = 3\sqrt{21}\)

Break down the radicands into their square factors:

1. \(\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5}\)
2. \(\sqrt{21}\) cannot be simplified further.

Combine the simplified terms:

\[ 3\sqrt{5} - 3\sqrt{21} \]

Final Answer