Which of the following is the compound surd:
(a) $4 \sqrt{3}$
(b) $\sqrt{3}$
(c) $2 \sqrt[4]{5}$
(d) $\sqrt{3}+\sqrt{5}-\sqrt{7}$

Given :

The given surds are 
 (a) $4 \sqrt{3}$

(b) $\sqrt{3}$

(c) $2 \sqrt[4]{5}$

(d) $\sqrt{3}+\sqrt{5}-\sqrt{7}$

To do :

We have to choose the compound sued from the given surds.

Solution :

Compound surd:

The algebraic sum of two or more simple surds or the algebraic sum of a rational number and simple surds is called the compound surd.

From the given surds,

$4 \sqrt{3}$, $\sqrt{3}$, $2 \sqrt[4]{5}$ are simple surds.

Therefore,  $\sqrt{3}+\sqrt{5}-\sqrt{7}$ is a compound surd.

Option (d) is correct.

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Updated on: 10-Oct-2022

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