Question

question
express in simplest radical form.
\sqrt{90}

Explanation:

Step1: Factor 90 into prime factors

We know that \(90 = 9\times10\), and \(9 = 3^2\), \(10=2\times5\). So \(90 = 3^2\times2\times5\).

Step2: Simplify the square root

Using the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0,b\geq0\)), we have \(\sqrt{90}=\sqrt{3^2\times2\times5}\).
According to the property \(\sqrt{a^2}=a\) (where \(a\geq0\)), \(\sqrt{3^2\times2\times5}=\sqrt{3^2}\times\sqrt{2\times5}\).
Since \(\sqrt{3^2} = 3\) and \(\sqrt{2\times5}=\sqrt{10}\), then \(\sqrt{90}=3\sqrt{10}\).

Answer:

\(3\sqrt{10}\)