Maths is a subject that can seem daunting to many students. There are so many formulas and concepts to learn, and it can be difficult to know where to start. In this blog post, we will take a look at one of the more confusing topics in maths- surds. We will explore what surds are, how to identify them, and how to simplify them. By the end of this post, you should have a better understanding of surds and feel confident in working with them!
What is a Surd in maths?
Surd in mathematics is an irrational number that cannot be expressed as a rational number. In other words, it is a number that cannot be expressed as a fraction p/q for any integers p and q. Surds are often represented using square root symbols or radicals, such as √3 or 3.
The term “surd” comes from the Latin word surdus, which means “deaf” or “silent.” This is because the decimal expansion of a surd is usually non-terminating and non-repeating. As a result, it cannot be expressed using finitely many decimals.
Surds can be found throughout mathematics, and they play an important role in algebra and calculus. Many famous mathematical results, such as the Quadratic Formula, involve surds. In addition, some numbers, such as π (pi), are only known to us as approximations because they are impossible to express exactly as a rational number.
Consequently, surds are an important part of mathematics that helps us to understand and work with numbers that we cannot express exactly.
How to Identify Surd?
To identify a surd, look for an expression that cannot be simplified or written as a fraction. Surds are often represented by the symbol “√” followed by the number or expression that cannot be simplified. For example, √9 is a surd because it cannot be simplified to 3/3 or any other rational number.
When solving equations with surds, it is often necessary to use approximation methods such as estimation. This is because it is not possible to obtain an exact answer when working with irrational numbers. However, by using estimation methods, it is possible to get a close approximation of the answer.
Estimating the value of a surd can be done by finding its nearest whole number or its nearest rational number. For example, if the value of √9 is required, the nearest whole number is 3 and the nearest rational number is 2.98 (which can be simplified to 3/1). Therefore, an estimate of the value of √9 would be either 3 or 2.98.
When working with equations that contain surds, it is important to remember that approximations will always be made when solving them. However, by using estimation methods, it is still possible to obtain a close result.
Conclusion
Surds are irrational numbers that cannot be expressed as a rational number, and are often represented using square root symbols or radicals. If you’re struggling to understand this concept, or any others, be sure to check out the Noon app. It has over 10,000 lectures on different subjects from the best teachers across the globe, so you’re bound to find something that can help you out. With such a wide range of topics available at your fingertips, there’s no excuse not to ace your next exam!