Question

9 radical24 - 5 radical6 + 3 radical54

Answer 1

To simplify the expression \(9 \sqrt{24} - 5 \sqrt{6} + 3 \sqrt{54}\), we can start by simplifying each radical.

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

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 substitute these simplified forms back into the expression:
\[
18 \sqrt{6} - 5 \sqrt{6} + 9 \sqrt{6}
\]

Next, combine the like terms:
\[
(18 - 5 + 9) \sqrt{6}
\]
Calculating the coefficients:
\[
18 - 5 = 13
\]
\[
13 + 9 = 22
\]

Thus, the expression simplifies to:
\[
22 \sqrt{6}
\]

So the final answer is:
\[
\boxed{22 \sqrt{6}}
\]