preform the indicated operation. be sure to rationalize the denominator when necessary.make sure to simplify as much as possible and givw the exact answer (this means NO decimals since decimals is rounding!)

Question

4 square root of 6 +square root of 54

Answer 1

To simplify the expression \( 4\sqrt{6} + \sqrt{54} \), we first need to simplify \( \sqrt{54} \).

1. Simplifying \( \sqrt{54} \):

   • We can factor \( 54 \) into \( 9 \times 6 \).
   • Thus, we have: \[ \sqrt{54} = \sqrt{9 \times 6} = \sqrt{9} \cdot \sqrt{6} = 3\sqrt{6} \]

2. Substituting back into the expression: \[ 4\sqrt{6} + \sqrt{54} = 4\sqrt{6} + 3\sqrt{6} \]

3. Combining like terms: \[ (4 + 3)\sqrt{6} = 7\sqrt{6} \]

The final simplified answer is: \[ \boxed{7\sqrt{6}} \]