Question
Question Express in simplest radical form. \[ \sqrt{54}-7 \sqrt{6} \]
Ask by Weston Mcdonald. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplest radical form of the expression is \(-4\sqrt{6}\).
Solution
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To simplify \(\sqrt{54}\), we can break it down. We know that \(54 = 9 \times 6\), and since \(\sqrt{9} = 3\), we can rewrite \(\sqrt{54}\) as: \[ \sqrt{54} = \sqrt{9 \times 6} = \sqrt{9} \cdot \sqrt{6} = 3\sqrt{6} \] Now, substituting back into the original expression gives us: \[ 3\sqrt{6} - 7\sqrt{6} \] Now we can combine like terms: \[ (3 - 7)\sqrt{6} = -4\sqrt{6} \] Thus, the expression in simplest radical form is: \[ \boxed{-4\sqrt{6}} \]
