Question

question
what is the product of 6 and ( 3sqrt{54} ) in simplest radical form?

Explanation:

Step1: Multiply the coefficients

First, multiply the coefficients 6 and 3. So, \(6\times3 = 18\).

Step2: Simplify the radical

Now, simplify \(\sqrt{54}\). We can factor 54 as \(9\times6\), and since \(\sqrt{9\times6}=\sqrt{9}\times\sqrt{6}\) (by the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) for \(a\geq0,b\geq0\)), and \(\sqrt{9} = 3\), so \(\sqrt{54}=3\sqrt{6}\).

Step3: Multiply the result from Step1 and Step2

Now, multiply 18 (from Step1) with \(3\sqrt{6}\) (from Step2). So, \(18\times3\sqrt{6}=54\sqrt{6}\).

Answer:

\(54\sqrt{6}\)