Surds

Surds are real numbers involving roots for which there is no exact value. For example Ö2 and Ö3. Surds are also irrational numbers, i.e. they cannot be expressed in the form . When put in decimal form, irrational numbers neither terminate nor recur. For example : Ö2 = 1.41423..... . When surds appear in an answer, thay are accepted, and the answer is said to be in its simplest form.

Rules :

1. (Öa)(Öb) =
2. =

Surd Conjugates :

(a + Öb) and (a - Öb) are surd conjugates.

Note : Öa is its surd conjugate in itself.

Rationalisation :

When surds appear as denominators in a fraction, the fraction can be simplified by removing the surd from the denominator. This is achieved by multiplying the numerator and the denominator by the surd conjugate. This process is called rationalisation.

Example :

  

  

  = 3(2 + Ö3)

---