Question

simplify. assume s is greater than or equal to zero. $10sqrt{75s^{9}}$

Explanation:

Step1: Factor the radicand

Factor \(75s^9\) into perfect squares and remaining factors. \(75 = 25\times3\) and \(s^9 = s^8\times s\), so \(75s^9=25\times3\times s^8\times s\).
\[10\sqrt{25\times3\times s^8\times s}\]

Step2: Simplify the square root

Use the property \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (\(a\geq0,b\geq0\)) and \(\sqrt{a^2}=a\) (\(a\geq0\)). \(\sqrt{25}=5\), \(\sqrt{s^8}=s^4\) (since \(s\geq0\)).
\[10\times\sqrt{25}\times\sqrt{s^8}\times\sqrt{3s}=10\times5\times s^4\times\sqrt{3s}\]

Step3: Multiply the constants

Multiply \(10\) and \(5\).
\[50s^4\sqrt{3s}\]

Answer:

\(50s^{4}\sqrt{3s}\)