Question

simplify.
$10\sqrt{12}$

Explanation:

Step1: Factor the radicand

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

Step2: Use the property of square roots

According to the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0,b\geq0\)), 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

Now we have \(10\sqrt{12}=10\times2\sqrt{3}\).

Step4: Calculate the product

\(10\times2\sqrt{3}=20\sqrt{3}\).

Answer:

\(20\sqrt{3}\)