Question

question 3 of 5

select the correct answer.

what is the simplified form of this expression?
\\(5\sqrt{54} - 3\sqrt{24}\\)

\\(33\sqrt{6}\\)
\\(8\sqrt{6}\\)
\\(21\sqrt{6}\\)
\\(9\sqrt{6}\\)

Explanation:

⚡ Using what you learned: simplifying radical expressions

Step 1: Simplify the first radical term

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

Step 2: Simplify the second radical term

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

Step 3: Subtract the simplified terms

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

Answer:

\( 9\sqrt{6} \) (the fourth option)