Question

simplify \\(\sqrt{300}\\)

Explanation:

Step1: Factor 300

Find the largest perfect square factor of 300. We know that \(300 = 100\times3\), where 100 is a perfect square (\(10^2\)).

Step2: Apply square - root property

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\)), we have \(\sqrt{300}=\sqrt{100\times3}=\sqrt{100}\times\sqrt{3}\).
Since \(\sqrt{100} = 10\), then \(\sqrt{300}=10\sqrt{3}\).

Answer:

\(10\sqrt{3}\)