Question Express in simplest radical form. $$ \sqrt{54}-7 \sqrt{6} $$

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UpStudy AI · Accepted Answer

1. Write the expression:  
   $$
   \sqrt{54} - 7\sqrt{6}.
   $$

2. Simplify $$\sqrt{54}$$ by finding perfect square factors. Note that $$54 = 9 \times 6$$ and $$9$$ is a perfect square:
   $$
   \sqrt{54} = \sqrt{9 \times 6} = \sqrt{9}\sqrt{6} = 3\sqrt{6}.
   $$

3. Substitute the simplified form back into the expression:
   $$
   3\sqrt{6} - 7\sqrt{6}.
   $$

4. Combine like terms (both terms have $$\sqrt{6}$$):
   $$
   (3 - 7)\sqrt{6} = -4\sqrt{6}.
   $$

The final answer in simplest radical form is:  
$$
-4\sqrt{6}.
$$
The simplest radical form of the expression is $$-4\sqrt{6}$$.

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Express in simplest radical form.

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