Combine the radicals using addition and subtraction, if possible. 9√24 - 5√6 + 3√54? (1 point) Responses

Question

226–√ 22
Unlike radicals cannot be combined using addition and subtraction.
42√2
4√6

Answer 1

To combine the radicals in the expression \(9\sqrt{24} - 5\sqrt{6} + 3\sqrt{54}\), we first simplify each radical where possible.

1. Simplifying \( \sqrt{24} \): \[ \sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \cdot \sqrt{6} = 2\sqrt{6} \] Therefore, \[ 9\sqrt{24} = 9 \cdot 2\sqrt{6} = 18\sqrt{6} \]

2. Simplifying \( \sqrt{54} \): \[ \sqrt{54} = \sqrt{9 \times 6} = \sqrt{9} \cdot \sqrt{6} = 3\sqrt{6} \] Thus, \[ 3\sqrt{54} = 3 \cdot 3\sqrt{6} = 9\sqrt{6} \]

Now we can rewrite the original expression: \[ 9\sqrt{24} - 5\sqrt{6} + 3\sqrt{54} = 18\sqrt{6} - 5\sqrt{6} + 9\sqrt{6} \]

Now combine the like terms: \[ 18\sqrt{6} - 5\sqrt{6} + 9\sqrt{6} = (18 - 5 + 9)\sqrt{6} = 22\sqrt{6} \]

Thus, the final result is: \[ \boxed{22\sqrt{6}} \]