十年级是英国初中教育最关键的一年，它综合了九年级已经学习过的数学知识，在九年级的基础上，对知识点进行深化学习，提高题目难度，所以对于九年级基础不牢固的同学，可能在十年级考试中会出现成绩大幅度的下滑。为了避免此类情况的发生，我们需要做好准备，下面为大家整理了大部分十年级可能会遇到的重难点问题，请大家在预习，学习，复习的时候都请认真对待。−2+3√2+2√3−√6

（一）二次根式的应用Application of quadratic surds

             1.明白何为二次根式。(通过思考固定面积正方形的边长来做更加形象的记忆) 代表了面积为x的正方形边长。

             Understand what is a quadratic surd. (Do a more vivid memory by thinking about the side length of a square with a constant area) represents                   the side length of a square with area x.

             2.二次根式各类题型的总结。其中主要包括 化简复杂二次根式，合并同类二次根式，分母有理化，复杂分母有理化等等。例题如下：                                         A summary of various types of questions in quadratic radicals. It mainly includes: simplifying complex quadratic radicals, merging similar quadratic radicals, rationalizing denominators, rationalizing complex denominators, and so on. Example questions are as follows:

                ①. Simplify    

                ②. Simplify  +++

                ③.Simplify  

大家在处理类似问题的时候要牢记，二次根式的运算法则，具体列举如下：

①二次根式内的常数具有非负性：Constants in quadratic radicals have non-negativity:

②乘法和积的算术平方根可互相转化: Arithmetic square roots of multiplication and product are interchangeable:

③除法和商的算术平方根可互相转化:The arithmetic square roots of division and quotient are interchangeable:

④在处理加减法时，只能做合并同类项处理，千万不可以犯的严重错误，因为这两个根式本质上是不同的两个整体。

When dealing with addition and subtraction, you can only deal with collecting similar items. Never make a serious mistake of , because the essence of these two radicals are two different wholes.

关于以上问题的答案，我会在下一讲，指数的重要性质里公布，大家如果有不懂的问题，也可以来问我。二次根式作为二次函数的基础，作为我们同学在数学中第一个与无理数密切相关的知识点，一方面它是数学真正难点的基础，一方面也是我们同学将所认识的数集从有理数向实数拓展的重要步骤。大家一定要多多练习，这样才能在11月的年终考试中拿到好成绩。

Regarding the answers to the above questions, I will announce them in the next lecture, The Important Nature of Indexes. If you have any questions you don’t understand, you can also ask me. As the basis of quadratic function, quadratic radical is the first knowledge point closely related to irrational numbers in mathematics. On the one hand, it is the basis of the real difficulty of mathematics. On the other hand, it is also an important step for students to expand the set of numbers they know from rational numbers to real numbers. You must practice a lot so that you can get good grades in the year-end exams in November.