
1. Surd or Radical: If 'n' is a natural number and 'a' is a positive rational number such that ^{n}Ö a = a^{1/n} is not a rational number, then ^{n}Öa is called a surd of n^{th} order.
2. Simple surd:
3. Mixed surd:
4.Compound Surd:
5. Binomial Surd:
6. Similar Surd:
7. Dissimilar Surds:
8. Order of the surd:
9. Laws of Radicals: 10. Comparison of surds is possible only when they are of the same order, then the radicals are to be compared. 11. When the surds to be multiplied or divided are not of the same order, they have to be necessarily brought to same order before the required operation is done. 12. If the product of two surds is national then each of the two surds is called the rationalizing factor of the other. 13. The rationalizing factor of a given surd is not unique. 14. It is always convenient to use the simplest of all rationalizing factors of a given surd. 15. Quadratic surds are the surds of second order. 16. Two binomial expressions containing surds differing only conjugate each other.
17. If the product of two mixed surds a + Öb and a  Öb,
where a and b Î, is a rational number then a + Öb and a 
Öb are called conjugate surds to each other. 