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

Jun 05, 2023

Jun 01, 2023

May 21, 2023

May 16, 2023

May 10, 2023

Latest Math Problems

Jun 08, 2023

May 09, 2023

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

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

A math help place with list of solved problems with answers and worksheets on every concept for your practice.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved