1Cademy - Like Radicals

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Index of the Radical

Definition

Like Radicals

Radicals are classified as like radicals when they share both the same index and the same radicand. Both conditions must hold simultaneously — if either the index or the radicand differs, the radicals are not like.

For example:

$9\sqrt[4]{42x}$ and $-2\sqrt[4]{42x}$ are like radicals because both have index $4$ and radicand $42x$ .
$5\sqrt[3]{125x}$ and $6\sqrt[3]{125y}$ are not like radicals because, although both have index $3$ , their radicands differ ( $125x$ versus $125y$ ).
$2\sqrt[5]{1000q}$ and $-4\sqrt[4]{1000q}$ are not like radicals because, although both have radicand $1000q$ , their indices differ ( $5$ versus $4$ ).

This definition generalizes the concept of like square roots. Because all square roots share the index $2$ , like square roots need only matching radicands. For higher roots, the index must be checked as well.

Updated 2026-05-01

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