Question

simplify or evaluate the expression ( 3sqrt{18} )

Explanation:

Step1: Simplify the square root

Factor 18 into \(9\times2\), so \(\sqrt{18}=\sqrt{9\times2}\). By the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\)), we get \(\sqrt{9\times2}=\sqrt{9}\times\sqrt{2}=3\sqrt{2}\).

Step2: Multiply by the coefficient

Now we have \(3\sqrt{18}=3\times(3\sqrt{2})\). Multiply the coefficients: \(3\times3 = 9\), so the result is \(9\sqrt{2}\). If we want a decimal approximation, \(\sqrt{2}\approx1.414\), then \(9\times1.414\approx12.726\). But the simplified radical form is \(9\sqrt{2}\).

Answer:

The simplified form of \(3\sqrt{18}\) is \(9\sqrt{2}\) (or approximately \(12.73\) if a decimal is preferred).