surd

简明释义

英[sɜːd]美[sɜːrd]

adj. 不尽根的；清音的；无道理的

n. 清音；不尽根；无理数

英英释义

单词用法

同义词

反义词

例句

1.Jade has the funtion of clean surd , stop thirsty , calm false asthma , calm mind , and nourish the viscera . it is a good medicine of pure gas , and it also may avoid dirty disease'gas.

玉具有清音哑，止烦渴，定虚喘，安神明，滋养五脏六腑的作用，是具有清纯之气的良药，可避秽浊之病气。

2.But I don't think so; in view of the fact I'm not quite surd.

但不这样认为，鉴于事实说明，我不相信是这样。

3.Jade has the funtion of clean surd , stop thirsty , calm false asthma , calm mind , and nourish the viscera . it is a good medicine of pure gas , and it also may avoid dirty disease'gas.

玉具有清音哑，止烦渴，定虚喘，安神明，滋养五脏六腑的作用，是具有清纯之气的良药，可避秽浊之病气。

4.The square root of 2 is a surd because it cannot be expressed as a fraction.

2的平方根是一个surd，因为它无法表示为分数。

5.Many students struggle with simplifying surd expressions in algebra.

许多学生在代数中简化surd表达式时感到困难。

6.Calculating the area of a circle involves using the surd for pi.

计算圆的面积涉及使用π的surd。

7.In mathematics, a surd is often used to indicate irrational numbers.

在数学中，surd常用于表示无理数。

8.To simplify the equation, we need to rationalize the surd in the denominator.

为了简化方程，我们需要使分母中的surd有理化。

作文

In the realm of mathematics, particularly in algebra and geometry, we often encounter various types of numbers. One such category is that of surd, which refers to an expression containing a root that cannot be simplified into a rational number. For instance, the square root of 2 is a classic example of a surd. It is an irrational number, meaning it cannot be expressed as a fraction of two integers. Understanding surd is crucial for students as it lays the foundation for more advanced mathematical concepts.The significance of surd extends beyond mere definitions; it plays a vital role in various mathematical operations and problem-solving scenarios. When dealing with equations that involve roots, recognizing surd can help in simplifying expressions and making calculations more manageable. For example, when you encounter the expression √18, it can be simplified to 3√2, where √2 remains a surd. This process not only aids in simplification but also enhances one’s ability to work with irrational numbers effectively.Moreover, surd appears frequently in geometry, especially in the calculation of areas and volumes. The Pythagorean theorem, which is fundamental in determining the lengths of sides in right triangles, often involves surd values. For instance, if one side of a triangle measures 3 units and the other side measures 4 units, the length of the hypotenuse can be calculated using the equation c = √(3² + 4²), resulting in c = 5. However, if the sides were different, say 1 and √3, the hypotenuse would involve a surd as well, demonstrating its importance in practical applications.In addition to its mathematical implications, surd also has philosophical undertones. The concept of irrationality, represented by surd, challenges our understanding of numbers and their properties. It prompts us to ponder the nature of infinity and the limitations of human comprehension. The existence of surd numbers reminds us that not all quantities can be neatly packaged into rational forms, reflecting the complexity and beauty of mathematics.Furthermore, the study of surd can enhance critical thinking skills. Engaging with irrational numbers encourages students to think outside the box and approach problems from different angles. It fosters a mindset that values exploration and creativity, essential traits in both academic and real-world scenarios. As students learn to manipulate surd, they develop a deeper appreciation for the intricacies of mathematics and its applications.In conclusion, the term surd is more than just a mathematical jargon; it represents a significant concept that permeates various aspects of mathematics and beyond. From simplifying expressions to understanding geometric principles, surd is integral to a comprehensive mathematical education. Embracing the challenges posed by surd can lead to greater mathematical proficiency and a richer understanding of the world around us. As we continue to explore the depths of mathematics, let us appreciate the role of surd and its contribution to our knowledge and understanding of numbers.

在数学领域，特别是代数和几何中，我们经常遇到各种类型的数字。其中一个类别是surd，它指的是包含无法简化为有理数的根的表达式。例如，2的平方根就是一个经典的surd例子。它是一个无理数，意味着它不能被表示为两个整数的分数。理解surd对学生来说至关重要，因为它为更高级的数学概念奠定了基础。surd的重要性不仅仅限于定义；它在各种数学运算和问题解决场景中发挥着关键作用。当处理涉及根的方程时，识别surd可以帮助简化表达式，使计算变得更可管理。例如，当你遇到表达式√18时，它可以简化为3√2，其中√2仍然是一个surd。这个过程不仅有助于简化，还增强了人们有效处理无理数的能力。此外，surd在几何学中也经常出现，尤其是在计算面积和体积时。毕达哥拉斯定理在确定直角三角形边长时，通常涉及surd值。例如，如果一个三角形的一条边长为3单位，另一条边长为4单位，则可以使用公式c = √(3² + 4²)来计算斜边的长度，结果为c = 5。然而，如果边长不同，比如1和√3，斜边也会涉及到surd，这展示了它在实际应用中的重要性。除了数学含义，surd还有哲学上的深意。无理性的概念由surd所代表，挑战了我们对数字及其性质的理解。它促使我们思考无限的本质和人类理解的局限性。surd数字的存在提醒我们，并非所有数量都可以整齐地包装成有理形式，反映了数学的复杂性和美丽。此外，研究surd可以增强批判性思维能力。与无理数的接触鼓励学生跳出框架，从不同角度看待问题。它培养了一种重视探索和创造力的思维方式，这在学术和现实世界中都是必不可少的特质。当学生学习操作surd时，他们对数学的复杂性和应用有了更深刻的欣赏。总之，术语surd不仅仅是数学术语；它代表了一个重要的概念，渗透到数学的各个方面及其之外。从简化表达式到理解几何原理，surd是全面数学教育的核心。接受surd带来的挑战可以导致更高的数学能力和对周围世界更丰富的理解。在我们继续探索数学的深度时，让我们欣赏surd的角色及其对我们知识和数字理解的贡献。