求 $(3+x)\sqrt{1+4x}$ 的二项展开式中 $x^3$ 的系数。

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

乘积中的三次项来自 $3$ 乘根式的三次项，以及 $x$ 乘根式的二次项。把两个二项系数完整写出。

In the expansion of $(1+4x)^{1/2}$, the $x^2$ term is

and the $x^3$ term is

Therefore the $x^3$ term in $(3+x)\sqrt{1+4x}$ is

The coefficient is $\boxed{10}$.