Question

simplify:\\\\$\sqrt{27}$

Explanation:

Step1: Factor 27 into prime factors

We know that \(27 = 9\times3\), and \(9 = 3^2\). So we can rewrite \(\sqrt{27}\) as \(\sqrt{9\times3}\).

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

Applying this property, we get \(\sqrt{9\times3}=\sqrt{9}\times\sqrt{3}\).

Step3: Simplify \(\sqrt{9}\)

Since \(3^2 = 9\), then \(\sqrt{9}=3\). So \(\sqrt{9}\times\sqrt{3}=3\sqrt{3}\).

Answer:

\(3\sqrt{3}\)