Question

question 2

simplify the expression.

(2\sqrt{24} - \sqrt{2} - 3\sqrt{18} - \sqrt{8})

\\(4\sqrt{6} - 11\sqrt{2}\\)
\\(4\sqrt{6} - 10\sqrt{2}\\)
\\(4\sqrt{6} - 12\sqrt{2}\\)
\\(8\sqrt{6} - 12\sqrt{2}\\)

Explanation:

⚡ Using what you learned: Simplifying radical expressions

Step 1: Simplify each radical term

Find perfect square factors for each radicand:

• \(2\sqrt{24} = 2\sqrt{4 \cdot 6} = 2 \cdot 2\sqrt{6} = 4\sqrt{6}\)
• \(\sqrt{2}\) is already in simplest form.
• \(3\sqrt{18} = 3\sqrt{9 \cdot 2} = 3 \cdot 3\sqrt{2} = 9\sqrt{2}\)
• \(\sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2}\)

Step 2: Substitute and combine like terms

Substitute the simplified radicals back into the original expression:

$$ 4\sqrt{6} - \sqrt{2} - 9\sqrt{2} - 2\sqrt{2} $$

Combine the like terms containing \(\sqrt{2}\):

$$ 4\sqrt{6} - (1 + 9 + 2)\sqrt{2} = 4\sqrt{6} - 12\sqrt{2} $$

Answer:

\(4\sqrt{6} - 12\sqrt{2}\)