Question

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what is the product of 2 and 4√147 in simplest radical form?
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√

Explanation:

Step1: Multiply the coefficients

First, multiply the coefficients 2 and 4. So, \(2\times4 = 8\).

Step2: Simplify the radical

Now, simplify \(\sqrt{147}\). We can factor 147 as \(49\times3\), since \(49\times3 = 147\). Then, \(\sqrt{147}=\sqrt{49\times3}\). Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a = 49\) and \(b = 3\)), we get \(\sqrt{49}\times\sqrt{3}\). Since \(\sqrt{49}=7\), this simplifies to \(7\sqrt{3}\).

Step3: Multiply the result from Step1 and Step2

Now, multiply the 8 from Step1 with \(7\sqrt{3}\) from Step2. So, \(8\times7\sqrt{3}=56\sqrt{3}\).

Answer:

\(56\sqrt{3}\)