Question

simplify.
$10\sqrt{147}$

Explanation:

Step1: Factor 147 into prime factors

We need to factor 147 to simplify the square root. We know that \(147 = 49\times3\), and \(49 = 7^2\). So, \(147=7^2\times3\).

Step2: Simplify the square root

Using the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a = 7^2\) and \(b = 3\)), we have \(\sqrt{147}=\sqrt{7^2\times3}=\sqrt{7^2}\times\sqrt{3}\). Since \(\sqrt{7^2} = 7\), then \(\sqrt{147}=7\sqrt{3}\).

Step3: Multiply by the coefficient outside the square root

We have \(10\sqrt{147}\), and we just found that \(\sqrt{147}=7\sqrt{3}\). So, \(10\sqrt{147}=10\times7\sqrt{3}\).

Step4: Calculate the product of the coefficients

\(10\times7 = 70\), so \(10\sqrt{147}=70\sqrt{3}\).

Answer:

\(70\sqrt{3}\)