Question

simplify. assume s is greater than or equal to zero. \\(sqrt{45s^{3}}\\)

Explanation:

Step1: Factor the radicand

We can factor \(45s^3\) into factors that are perfect squares. \(45 = 9\times5\) and \(s^3 = s^2\times s\). So, \(\sqrt{45s^3}=\sqrt{9\times5\times s^2\times s}\).

Step2: Use the property of square roots

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0\) and \(b\geq0\)), we can split the square root: \(\sqrt{9\times5\times s^2\times s}=\sqrt{9}\times\sqrt{s^2}\times\sqrt{5s}\).
Since \(s\geq0\), \(\sqrt{9} = 3\) and \(\sqrt{s^2}=s\). So, substituting these values in, we get \(3\times s\times\sqrt{5s}=3s\sqrt{5s}\).

Answer:

\(3s\sqrt{5s}\)