Question

simplify.\sqrt{315}

Explanation:

Step1: Factor 315 into prime factors

First, we factorize 315. We know that \(315 = 9\times35\), and further, \(9 = 3^2\), \(35=5\times7\). So, \(315 = 3^2\times5\times7\).

Step2: Use the property of square roots \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (\(a\geq0,b\geq0\))

We can rewrite \(\sqrt{315}\) as \(\sqrt{3^2\times5\times7}\). According to the property \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\), we can split this into \(\sqrt{3^2}\times\sqrt{5\times7}\).

Step3: Simplify \(\sqrt{3^2}\)

Since \(\sqrt{3^2}=3\) (because the square root of a square of a non - negative number is the number itself), we get \(3\sqrt{35}\).

Answer:

\(3\sqrt{35}\)