Surds- Introduction & simplifying

Surds - Introduction

Surds are numbers left in ‘square root form’ (or ‘cube root form’ etc). They are therefore irrational numbers which can’t be written as a fraction and have an infinite decimal part.
They are used when exact values are needed. Examples are √2, √3, √5, √11, etc.
Although they can’t be simplified to a rational number, they can often be simplified to a simpler surd.

Simplifying Surds

Simplifying a surd involves breaking it down to its simplest form.
This is done by finding the largest square number (for square roots) or cube number (for cube roots) that divides exactly into the number under the root sign, and simplifying it from there.

Parts of Surds

A surd has two main parts: the radical sign (√) and the radicand (the number under the root).
The value of the square root is called the root. The square root of 4 is 2, so we say that the root of 4 is 2.

Usage of Surds

Surds are often used in geometry and trigonometry, where they aid in exact calculations.
They are helpful in preserving the exact values in computations, especially in scientific and engineering problems where high precision is needed.

Examples

For example, √18 can be simplified to 3√2, as 18 = 9 x 2 and √9 = 3.
As another example, √200 can be simplified to 10√2, as 200 = 100 x 2 and √100 = 10.

Conclusion

Surds are often mistaken to be overly complex but grasping the concept hinges on understanding the definition and usage.
Understanding surds and knowing how to simplify them is an essential part of algebra. The process of simplifying surds is a necessary skill in many areas of mathematics and is fundamental in extending to higher-level mathematics. Regular practice with simplifying surd expressions will increase your confidence and proficiency with these number types.