Question

question
express in simplest radical form.
\\(\dfrac{\sqrt{180}}{6}\\)

Explanation:

Step1: Factor 180

Factor 180 into perfect square and other factor: \(180 = 36\times5\)

Step2: Simplify the square root

Simplify \(\sqrt{180}\) using \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (\(a = 36\), \(b = 5\)): \(\sqrt{180}=\sqrt{36\times5}=\sqrt{36}\times\sqrt{5}=6\sqrt{5}\)

Step3: Substitute and simplify the fraction

Substitute \(\sqrt{180}=6\sqrt{5}\) into \(\frac{\sqrt{180}}{6}\): \(\frac{6\sqrt{5}}{6}\)
Cancel out the 6 in numerator and denominator: \(\sqrt{5}\)

Answer:

\(\sqrt{5}\)