Question

simplify.
$10\sqrt{12}$

Explanation:

Step1: Factor 12 into perfect square and other

We know that \(12 = 4\times3\), where \(4\) is a perfect square. So we can rewrite \(\sqrt{12}\) as \(\sqrt{4\times3}\).
\[
\sqrt{12}=\sqrt{4\times3}
\]

Step2: Use square - root property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\))

According to the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a = 4,b=3\)), we have \(\sqrt{4\times3}=\sqrt{4}\times\sqrt{3}\). Since \(\sqrt{4} = 2\), then \(\sqrt{4}\times\sqrt{3}=2\sqrt{3}\).

Step3: Multiply with the coefficient 10

Now we have \(10\sqrt{12}=10\times\sqrt{12}\), and we just found that \(\sqrt{12} = 2\sqrt{3}\), so \(10\times2\sqrt{3}=20\sqrt{3}\).

Answer:

\(20\sqrt{3}\)