Question

simplify.
\sqrt{245}

Explanation:

Step1: Factor 245

We need to find the largest perfect square factor of 245. We know that \(245 = 49\times5\), where 49 is a perfect square (\(7^2\)).

Step2: Use square root property

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\)), we can rewrite \(\sqrt{245}\) as \(\sqrt{49\times5}\). Then, \(\sqrt{49\times5}=\sqrt{49}\times\sqrt{5}\). Since \(\sqrt{49} = 7\), we have \(7\sqrt{5}\).

Answer:

\(7\sqrt{5}\)