In chapter 2, you studied about the concept of base and index and laws of indices. In this sub topic, you will learn about surds which are numbers whose square roots cannot be determined in terms of rational numbers.

Square roots of numbers that cannot be simplified into whole numbers are called surds. Irrational numbers which are in the form of roots are called surds. For example,

are irrational numbers while

are rational numbers.

Surds are nothing but square root representation of irrational numbers that cannot be expressed in fractional or recurring decimals

As we can see from the above example, the surds have a decimal which goes on forever without repeating, and that makes them irrational numbers.

Key Point

• If a positive whole number is not a perfect square, then its square root is called a surd. A surd cannot be written as a fraction.
• A surd is an example of an irrational number.