Question
Express in simplest radical form. \[ \frac{\sqrt{180}}{6} \]
Ask by Kelley Evans. in the United States
Jan 23,2025
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\(\sqrt{5}\)
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To simplify \(\frac{\sqrt{180}}{6}\), we start with simplifying \(\sqrt{180}\). We can factor \(180\) into its prime factors: \[ 180 = 36 \times 5 = 6^2 \times 5 \] Thus, \[ \sqrt{180} = \sqrt{36 \times 5} = \sqrt{36} \times \sqrt{5} = 6\sqrt{5} \] Now, substituting this back into the original expression: \[ \frac{\sqrt{180}}{6} = \frac{6\sqrt{5}}{6} = \sqrt{5} \] Therefore, the expression in simplest radical form is \[ \sqrt{5} \]