A surd of represents the entire quantity under the root symbol is called an entire surd.

The part of the multiplying factor of a quantity under the root can be taken out from the root in some cases but the entire number is displayed under the root. Hence, the surd is known as an entire surd. The entire surd is purely a surd. For this reason, the entire surd is also called as a pure surd.

$(1)\,\,\,\,\,\,$ $\sqrt{8}$

Express the number $8$ as multiplying factors of $2$.

$\implies \sqrt{8} = \sqrt{2 \times 2 \times 2} = \sqrt{2^2 \times 2}$

$\implies \sqrt{8} = \sqrt{2^2} \times \sqrt{2}$

$\implies \sqrt{8} = 2 \sqrt{2}$

In this example, $\sqrt{8}$ can be expressed as $2\sqrt{2}$ but it is expressed purely as a surd by displaying it as $\sqrt{8}$. Hence, the surd $\sqrt{8}$ is called as an entire surd or pure surd in mathematics.

$(2)\,\,\,\,\,\,$ $\sqrt[\displaystyle 3]{81}$

$(3)\,\,\,\,\,\,$ $\sqrt[\displaystyle 4]{343}$

$(4)\,\,\,\,\,\,$ $\sqrt[\displaystyle 5]{78125}$

$(5)\,\,\,\,\,\,$ $\sqrt[\displaystyle 6]{9765625}$

If any surd contains no multiplying factor outside the root, call the surd as an entire surd or pure surd.

Latest Math Topics

Jan 06, 2023

Jan 03, 2023

Jan 01, 2023

Dec 26, 2022

Dec 08, 2022

Latest Math Problems

Jan 31, 2023

Nov 25, 2022

Nov 02, 2022

Oct 26, 2022

A best free mathematics education website for students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Learn how to solve the maths problems in different methods with understandable steps.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved