Question

simplify.
\sqrt{245}

Explanation:

Step1: Factor 245

We need to find the largest perfect square factor of 245. The factors of 245 are \(1, 5, 7, 35, 49, 245\). Among these, 49 is a perfect square (\(7^2 = 49\)) and \(245=49\times5\). So we can rewrite \(\sqrt{245}\) as \(\sqrt{49\times5}\).

Step2: Use square - root property

Using the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a = 49\) and \(b = 5\) and \(a\geq0,b\geq0\)), we have \(\sqrt{49\times5}=\sqrt{49}\times\sqrt{5}\).
Since \(\sqrt{49} = 7\) (because \(7\times7 = 49\)), then \(\sqrt{49}\times\sqrt{5}=7\sqrt{5}\).

Answer:

\(7\sqrt{5}\)