Question

question
express in simplest radical form.
\\(\dfrac{\sqrt{20}}{10}\\)

Explanation:

Step1: Factor the radicand

Factor 20 into a product of a perfect square and another number: \(20 = 4\times5\), so \(\sqrt{20}=\sqrt{4\times5}\).

Step2: Simplify the square root

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\)), we have \(\sqrt{4\times5}=\sqrt{4}\times\sqrt{5}=2\sqrt{5}\). Now the expression becomes \(\frac{2\sqrt{5}}{10}\).

Step3: Simplify the fraction

Divide both the numerator and the denominator by their greatest common divisor, which is 2. So \(\frac{2\sqrt{5}\div2}{10\div2}=\frac{\sqrt{5}}{5}\).

Answer:

\(\frac{\sqrt{5}}{5}\)