simplify.\n$10\\sqrt{12}$

Explanation:

Step1: Factor the radicand

Factor 12 into a perfect square and another number: (12 = 4\times3), so (\sqrt{12}=\sqrt{4\times3}).

Step2: Use square root property

Using (\sqrt{ab}=\sqrt{a}\times\sqrt{b}) ((a\geq0,b\geq0)), we get (\sqrt{4\times3}=\sqrt{4}\times\sqrt{3}). Since (\sqrt{4} = 2), this becomes (2\sqrt{3}).

Step3: Multiply with the coefficient

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

Step4: Calculate the product

(10\times2 = 20), so the simplified form is (20\sqrt{3}).

Answer:

(20\sqrt{3})