Question

simplify (sqrt{72x})

Explanation:

Step1: Factor 72

Factor 72 into prime factors: \(72 = 36\times2\), and \(36 = 6^2\) (a perfect square). So \(72 = 6^2\times2\).

Step2: Apply square - root property

Using the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\)) and \(\sqrt{a^{2}} = a\) (\(a\geq0\)), we have:
\(\sqrt{72x}=\sqrt{6^{2}\times2\times x}=\sqrt{6^{2}}\times\sqrt{2x}\)
Since \(\sqrt{6^{2}} = 6\), then \(\sqrt{72x}=6\sqrt{2x}\)

Answer:

\(6\sqrt{2x}\)