What are Surds and how to compare them?

Here in this article detail is given that what are Surds and how to compare Surds.The surds are unresolved roots of a whole number,surds when simplified into a decimal number then the type of decimal we get is non-recurrent decimal number ,as an example √2= 1.4142135623730……, √3 =1.732050807568………, so in most of the real time methematical application to get a precise value we utilise surds and it is better to leave the result in the form of surds .Since Surds are non-recurrent decimal numbers so surds can not be written in the form of a fraction,it is that’s why surds are known as an irrational numbers.The roots $\boldsymbol{\sqrt{5},\sqrt[3]{4}\: \: and\: \: \sqrt[4]{7}}$ etc are the examples of surds.

In straight way we can say Surds are an irrational number which cannot be represented in the form of fractions or recurring infinite decimals. So,in mathematical calculation it can be left as a roots. Surds are used in many real-time applications to make precise calculations. In this article, let us discuss different structures of surds and their simplification.

Surds are the roots of numbers which cannot be simplified into a whole or rational number. It cannot be accurately represented in a fraction. In other words, a surd is a root of the whole number that has an irrational value.

The surds are written in the form of $\boldsymbol{\sqrt[n]{x}}$ where n is called the radical or order of the surds and x is a whole number whose n^throots can not be resolved.

Surds can be converted in the form of exponents as following

$\boldsymbol{\sqrt[n]{x}}\boldsymbol{=x^{1/n}}$

$\boldsymbol{\sqrt[3]{4}}\boldsymbol{=4^{1/3}}$

$\boldsymbol{\sqrt[4]{6}}\boldsymbol{=6^{1/4}}$

$\boldsymbol{\sqrt[5]{8}}\boldsymbol{=8^{1/5}=\left ( 2^{3} \right )^{1/5}=2^{3/5}}$

The rational numbers and the surds of the same degree can be compared easily by a straightforward way but for comparing surds of different degrees you needed a special technic.

Surds of the same degree are known as equiradical surds and surds of unequal orders are known as non-equiradical surds.

Comparision of equiradical or same order of of surds:

$\boldsymbol{ex:\sqrt[n]{x},\: \sqrt[n]{y}}$