Combine the radicals using addition and subtraction, if possible.

Question

9√24−5√6+3√54 ?

(1 point)
Responses

422–√
42 square root of 2

226–√
22 square root of 6

46–√
4 square root of 6

Unlike radicals cannot be combined using addition and subtraction.
Unlike radicals cannot be combined using addition and subtraction.

Answer 1

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

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

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

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

Next, we combine the coefficients of \( \sqrt{6} \): \[ (18 - 5 + 9) \sqrt{6} = (22)\sqrt{6} \]

Thus, the simplified expression is: \[ 22\sqrt{6} \]

So the correct response is: 22 square root of 6.