Question

simplify.
\sqrt{315}

Explanation:

Step1: Factor 315

Factor 315 into prime factors: \(315 = 9\times35 = 9\times5\times7\), and \(9 = 3^2\). So \(315=3^2\times35\).

Step2: Apply square - root property

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a = 3^2\) and \(b = 35\)) and \(\sqrt{a^2}=a\) (for \(a\geq0\)), we have \(\sqrt{315}=\sqrt{3^2\times35}=\sqrt{3^2}\times\sqrt{35}=3\sqrt{35}\).

Answer:

\(3\sqrt{35}\)