Question

express in simplest radical form.
\\(\sqrt{98}\\)

Explanation:

Step1: Factor 98 into prime factors

We know that \(98 = 49\times2\), and \(49 = 7^2\). So we can rewrite \(\sqrt{98}\) as \(\sqrt{7^2\times2}\).

Step2: Use the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0,b\geq0\))

According to the property \(\sqrt{a^2\times b}=\sqrt{a^2}\times\sqrt{b}\) (since \(a = 7\geq0\) and \(b = 2\geq0\)), and we know that \(\sqrt{a^2}=a\) when \(a\geq0\). So \(\sqrt{7^2\times2}=\sqrt{7^2}\times\sqrt{2}=7\sqrt{2}\).

Answer:

\(7\sqrt{2}\)