Question

simplify.
\sqrt{147}

Explanation:

Step1: Factor 147 into prime factors

First, we factorize 147. We know that \(147 = 49\times3\), and \(49 = 7^2\). So we can rewrite \(\sqrt{147}\) as \(\sqrt{49\times3}\).

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

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\), we have \(\sqrt{49\times3}=\sqrt{49}\times\sqrt{3}\).
Since \(\sqrt{49} = 7\) (because \(7^2 = 49\)), then \(\sqrt{49}\times\sqrt{3}=7\sqrt{3}\).

Answer:

\(7\sqrt{3}\)