Question

multiply. write your answer in simplest form.\\(sqrt{2} cdot sqrt{147}\\)

Explanation:

Step1: Use property of square roots

Recall that \(\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}\) for \(a\geq0,b\geq0\). So, \(\sqrt{2}\cdot\sqrt{147}=\sqrt{2\times147}\).

Step2: Calculate the product inside the square root

Calculate \(2\times147 = 294\). So now we have \(\sqrt{294}\).

Step3: Factor 294 to simplify the square root

Factor 294: \(294 = 49\times6\), where 49 is a perfect square. So, \(\sqrt{294}=\sqrt{49\times6}\).

Step4: Use property of square roots again

Using \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (for \(a\geq0,b\geq0\)), we get \(\sqrt{49\times6}=\sqrt{49}\cdot\sqrt{6}\).

Step5: Simplify \(\sqrt{49}\)

Since \(\sqrt{49} = 7\), we have \(7\sqrt{6}\).

Answer:

\(7\sqrt{6}\)