Question

simplify
$sqrt{300}$
?

Explanation:

Step1: Factor 300 into perfect square and other

We know that \(300 = 100\times3\), where \(100\) is a perfect square (\(10^2\)). So, \(\sqrt{300}=\sqrt{100\times3}\).

Step2: Use square - root property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\))

According to the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a = 100\), \(b=3\)), we have \(\sqrt{100\times3}=\sqrt{100}\times\sqrt{3}\).
Since \(\sqrt{100} = 10\), then \(\sqrt{100}\times\sqrt{3}=10\sqrt{3}\).

Answer:

\(10\sqrt{3}\)