Question

quiz-- section 9.5
started: jun 26 at 2:47am
quiz instructions
for this quiz answer each question and select the best option
you have 20 minutes to complete the quiz.
you have only one attempt.

question 1
simplify the expression.
\\4\sqrt{12} + 3\sqrt{3} - 2\sqrt{48}\\

(a) \\(3\sqrt{3}\\)
(b) \\(5\sqrt{-33}\\)

Explanation:

⚡ Using what you learned: Simplifying radical expressions

Step 1: Simplify each radical term

Find perfect square factors for the numbers inside the square roots:

$$ 4\sqrt{12} = 4\sqrt{4 \cdot 3} = 4 \cdot 2\sqrt{3} = 8\sqrt{3} $$

$$ 3\sqrt{3} \text{ is already simplified} $$

$$ 2\sqrt{48} = 2\sqrt{16 \cdot 3} = 2 \cdot 4\sqrt{3} = 8\sqrt{3} $$

Step 2: Combine like terms

Substitute the simplified radicals back into the original expression:

$$ 8\sqrt{3} + 3\sqrt{3} - 8\sqrt{3} $$

Combine the coefficients:

$$ (8 + 3 - 8)\sqrt{3} = 3\sqrt{3} $$

Answer:

\( 3\sqrt{3} \)