Question

what is a surd and pure surd​

Answer 1

A surd in which the whole of the rational number is under the radical sign and makes the radicand, is called pure surd. In other words a surd having no rational factor except unity is called a pure surd or complete surd. For example, each of the surds √7, √10, √x, ∛50, ∛x, ∜6, ∜15, ∜x, 172/3, 595/7, m2/13 is pure surd.

Answer 2

Your question is divided into 2 parts.

Question :- 1  What is a Surd ?

Answer:- When roots of a non-negative number (quantities of type$\sqrt[n]{a}$, a being a rational number does not provide an exact solution, then this root is called a surd.

Example:- √2 , √5 , 3√8 , a + √b etc.

• All surds are irrational number.
• All irrational numbers are not surds.

Question :- 2 What is an Pure Surd ?

Answer:- Those surds which have factor other than 1, are known as mixed surd.

Example:- 3√5 , 4√6 , 7² , ∛5