Types of surds — lesson. Mathematics State Board, Class 9.

PDF chapter test TRY NOW

Surds can be classified into the following types. They are:

1. Surds of same order: Surds having the same root of index are called as surds of same order. They are also called as equiradical surds.

Example:

$\sqrt[3]{4}$ ,

$\sqrt[3]{7}$ and

$\sqrt[3]{13}$ are surds of same order having root index

$3$ .

2. Simplest form of a surd: When a surd is simplified and expressed as a product of rational and an irrational number, then the surd is said to be in simplest form. In the simplest form, the surd has

the smallest index of the radical.
the radical sign will have no fraction.
there will be no term of the form $a^n$ , where $a$ is a positive integer under index $n$ .

Example:

Write the surds

$\sqrt{12}$ and

$\sqrt[4]{64}$ in simplest form.

Solution:

$\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$

$\sqrt[4]{64} = \sqrt[4]{2 \times 2 \times 2 \times 2 \times 4} = 4\sqrt[4]{4}$

3. Pure and Mixed surds: If the coefficient of a surd is

$1$ , then the surd is said to be a pure surd. If the coefficient of a surd having other than

$1$ is called as mixed surd.

Example:

$\sqrt[3]{5}$ ,

$\sqrt{2}$ ,

$\sqrt[4]{7}$ are pure surds.

$2\sqrt[5]{16}$ ,

$3\sqrt[4]{9}$ ,

$7\sqrt[3]{5}$ are mixed surds.

4. Simple and compound surds: If a surd has only

$1$ term, then the surd is said to be a simple surd. The sum or difference of

$2$ or more surds is called as compound surd.

Example:

$\sqrt{3}$ ,

$4 \sqrt[3]{2}$ are simple surds.

$\sqrt[3]{5} + \sqrt[4]{13}$ ,

$\sqrt{5} - 7\sqrt[3]{8}$ are compound surds.

5. Binomial surd: The sum or difference of

$2$ terms which consists of either

$2$ surds or

$1$ is a rational number and an another is an irrational number is called as a binomial surd.

Example:

$\sqrt{7} - 6 \sqrt[3]{5}$ ,

$\frac{2}{7} + \sqrt[4]{13}$ are binomial surds.

Previous theory

Exit to the topic

Next theory

Send feedback

Did you find an error?

Send it to us!

4. Types of surds

Theory: