SURD

Surd is a manipulation of roots like



etc…and roots can be manipulated in different ways such as simplification, addition, subtraction, etc. Another name for surd is root.

Methods of Manipulating Surd

1. Simplification of Surd

2. Addition & Subtraction of Surd

3. Multiplication & Division of Surd

4. Conjugate of a Surd

General Rules for Solving Surd

1. Figures with figures and roots with roots.

2. When multiplying roots of similar values, you remove the roots and take only one of the values.

1. Simplification of Surd

Examples;

Simplify the following surd;

Solution

Split 

 



by searching for factors of 50 whereby at least one of them must be a perfect square.

Following this rule, the factors should be either 5 & 10 or 25 & 2 or 50 & 1 but 25 & 2 should be the most appropriate factor here because you can at least find the square root of 25 which makes it a perfect square.

Solution

Factors of 32 will be 16 & 2;

Note that at least one of the factors must be a perfect square.

Solution

 

Practice these questions below;