If a is a positive rational number, ‘n’ is positive integer and is an irrational number then is called a surd of degree ‘n’.
Conjugate Surd: If sum and product of two surds is a rational number then the two surds are called Conjugate surds to each other.
Ex: 5 + , 5 −
Rationalizing Factor: If the product of two surds is a rational number then two surds are called Rationalizing factors to each other.
Ex: + , −
Note: Every conjugate surd must be a rationalizing factor, but every rationalizing factor need not be a conjugate surd.
Standard forms of a Surd:
(where x + y = a, x . y = b)
(where x + y + z = a; x .y = b; y. z = c; z .x = d)