Question

simplify.
\sqrt{147}

Explanation:

Step1: Factor 147 into prime factors

We know that \(147 = 49\times3\), and \(49 = 7^2\), so \(147=7^{2}\times3\).

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

\(\sqrt{147}=\sqrt{7^{2}\times3}=\sqrt{7^{2}}\times\sqrt{3}\)

Step3: Simplify \(\sqrt{7^{2}}\)

Since \(\sqrt{a^{2}} = a\) for \(a\geq0\), then \(\sqrt{7^{2}} = 7\). So \(\sqrt{147}=7\sqrt{3}\)

Answer:

\(7\sqrt{3}\)