The word surd is used with reference to a root that is irrational. An irrational number is one which has a decimal that goes on forever but the digits do not repeat. This does not allow us to write an irrational number in the form a/b where a and b are integers.
For example sqrt(2) is a surd. It is equal to 1.4142135... which cannot be expressed as a/b for any integers a and b.
It has to be kept in mind that all roots are not surds, for example sqrt(4) = 2, cube root(27) = 3, etc.
A surd is term used to refer to an irrational root.
The terms "surds" is used when a number is irrational. Usually, we use this term when we prefer not calculate the square root or the cube root of a number because the number of decimals is large or iterative.
For instance, sqrt 2 is a surd but sqrt 9 = 3 is not.
To add two surds, the radicand must be the same:
sqrt 2 + sqrt 6
To multiply two surds is easy if the n-th root of both is the same.
When the surd is found at denominator of a fraction, w'e'll have to multiply it by it's conjugate, to change the surd denominator into a rational number.