Question

add or subtract, as indicated.

\\3\sqrt{24} - 5\sqrt{54}\\

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. \\3\sqrt{24} - 5\sqrt{54} = \\
(simplify your answer. type an exact answer, using radicals as needed.)

b. the expression is fully simplified.

Explanation:

⚡ Using what you learned: Roots and Radicals

Step 1: Simplify the first radical

$$ 3\sqrt{24} = 3\sqrt{4 \cdot 6} = 3 \cdot 2\sqrt{6} = 6\sqrt{6} $$

Step 2: Simplify the second radical

$$ 5\sqrt{54} = 5\sqrt{9 \cdot 6} = 5 \cdot 3\sqrt{6} = 15\sqrt{6} $$

Step 3: Subtract the simplified terms

$$ 6\sqrt{6} - 15\sqrt{6} = (6 - 15)\sqrt{6} = -9\sqrt{6} $$

Answer:

A. \(3\sqrt{24} - 5\sqrt{54} = -9\sqrt{6}\)