Blog

Parin Sir > Quantitative Aptitude (Maths) > Surds & Indices > Types of Surds > Types of Surds

Types of Surds

No Comments

■ Pure  Surd  :   A surd which consists wholly of  an irrational number is called a pure surd.

e.g. \sqrt{6} , \sqrt[4]{3}

■ Mixed  Surd  :   If a surd has one factor which is a rational number other than  1  and the other factor is an irrational number, then the surd is called a mixed surd.

e.g. 2\sqrt{3}, \frac{2}{3}\sqrt{7},-5\sqrt[3]{19}

Every mixed surd can be expressed as a pure surd. However,  a pure surd cannot always  be converted into a mixed one.

e.g., 2 \sqrt[3]{5}=\sqrt[3]{2^{3}\times 5}=\sqrt[3]{40}

■ Rationalization  :   If  two surds be such that their product is rational, either of  them is called the rationalization factor of  the other or they are known as complex conjugates of  each other. This method of  conversion of  a surd into a rational number is termed as Rationalization.

 e.g.  (i) The rationalization factor of  2 + \sqrt{3}  =  2  – \sqrt{3}

        (ii) The rationalization factor of  2 – \sqrt{3} =  2  +\sqrt{3}

       (iii) The rationalization factor of  2 – \sqrt[3]{5}  =   4  +  2\sqrt[3]{5}   + \sqrt[3]{25}

       (iv) The rationalization factor of  2 – 3 i  =  2  + 3 i

■ Binomial  Quadratic  Surd  :   A  binomial quadratic surd is a binomial in which the surds present are of  order 2. Such surds have rationalization factor as the conjugates.

 e.g.   The rationalization factor of  2 + \sqrt{3}  =  2  – \sqrt{3}

 

Click here to see examples

Share
online dakhla tutorial surds Examples educational formula SUMS maths sutra example mathematics sutr math ganit of concept Types proof Parin theorem sir theorems bhai definition Mehta definitions maheta fundamental classes basic class base education sum

Leave a Reply