Question

simplify this expression.

\\((2 - 5\sqrt{6}) \cdot 3\sqrt{2}\\)

\\(\bigcirc\\) \\(6\sqrt{2} - 15\sqrt{6}\\)
\\(\bigcirc\\) \\(6\sqrt{2} - 15\sqrt{12}\\)
\\(\bigcirc\\) \\(6\sqrt{2} - 8\sqrt{6}\\)
\\(\bigcirc\\) \\(6\sqrt{2} - 30\sqrt{3}\\)

Explanation:

Apply the distributive property

$$ (2 - 5\sqrt{6}) \cdot 3\sqrt{2} = 2 \cdot 3\sqrt{2} - 5\sqrt{6} \cdot 3\sqrt{2} $$

Multiply the terms

$$ 2 \cdot 3\sqrt{2} = 6\sqrt{2} $$

$$ 5\sqrt{6} \cdot 3\sqrt{2} = 15\sqrt{12} $$

$$ (2 - 5\sqrt{6}) \cdot 3\sqrt{2} = 6\sqrt{2} - 15\sqrt{12} $$

Simplify the radical term

$$ \sqrt{12} = \sqrt{4 \cdot 3} = 2\sqrt{3} $$

$$ 15\sqrt{12} = 15 \cdot 2\sqrt{3} = 30\sqrt{3} $$

$$ 6\sqrt{2} - 15\sqrt{12} = 6\sqrt{2} - 30\sqrt{3} $$

Answer:

• (A) \(6\sqrt{2} - 15\sqrt{6}\)
• (B) \(6\sqrt{2} - 15\sqrt{12}\)
• (C) \(6\sqrt{2} - 8\sqrt{6}\)
• (D) \(6\sqrt{2} - 30\sqrt{3}\) (Correct answer)