Introduction of Surds

Definitions :

1. Surd: Any number which is in the form of √ⁿa (nth root of a) where 'n' is a

   natural and 'a' a rational number which is not the nth root of any

   natural number is called a surd (or) or a radical.

     Ex: √2, 3√3, 4√5 .......... etc.

     Note:

     * 'n' is called the order of the surd.

     * 'a' is called the radicand of the surd.

     * ⁿ√ is called the radical of the surd.

     * Every surd has a rational part and an irrational part.

     * All perfect squares and perfect cubes are not surds.

2. Simple Surd: Any surd whose rational part in unity (one) is called a simple

      surd.

     Ex: √2, √3, √4 .......... etc.

     Note:

     * Simple surd is also called a 'Pure surd'.

3. Mixed Surd: Any surd whose rational part is not unity (one) is called a

    mixed surd.

     Ex: 2√2, 3√5, ⅔√2 .......... etc.

     Note:

     * Mixed surd is also called an impure surd.

4. Monomial Surd: Any surd which has atleast one term is called a monomial

 surd.

     Ex: √2, 3√3, 2√2, 3√3 .......... etc.

     Note:

     * Every simple surd and a mixed surd is called a monomial surd.

5. Binomial Surd: Any surd which is a combination of two surds is called a

 binomial surd.

     Ex: √2 + √3, 3√3+√2 .......... etc.

    *

6. Quadratic Surds: Any surd whose order is 2 is called a quadratic surd.

     Ex: √2, √3, √5, √7 .......... etc.

7. Cubic Surd: Any surd whose order is 3 is called a cubic surd.

     Ex: ³√2, ³√3, ³√5, ³√7 ..........etc.

8. Similar or Like Surds: Surds whose irrational parts are the same are called

 like surds.

 Note:

 * Like surds can be added.

 * Like surds can be subtracted.

 * Like surds can be divided.

 * Like surds can be multiplied.

9. Dissimilar or Unlike Surds : Surds whose irrational parts are not same are

 called unlike surds.

 Note :

 * Unlike surds cannot be added.

 * Unlike surds cannot be subtracted.

 * Unlike surds can be multiplied

 * Unlike surds can be divided.

10. Rationalisation : Any procedure in which irrationals (surds) gets converted

     into rationals is called rationalisation.

11. Rationalising Factor: A number (surd) which converts an irrational into a

     rational through multiplication is called a rationalising

     factor.

 Note :

  Surd Rationalising factor

  √a √a

  η√α √a

  √a+b √a-b

  a-√b a+√b

  √a+√b √a-√b

  m√a+n√b m√a-n√b