1Cademy - Like Square Roots

Learn Before

Radicand

Definition

Like Square Roots

Like square roots are square roots that share the same radicand — the expression under the radical sign. Just as like terms in algebra are terms with the same variable(s) raised to the same power(s), like square roots are identified by having identical radicands. For example, $\sqrt{3}$ and $\sqrt{3}$ are like square roots because both have the radicand $3$ . Similarly, $3\sqrt{x}$ and $8\sqrt{x}$ are like square roots because both contain $\sqrt{x}$ . When the radicand involves more than one variable, the radicals are like only if all variables and their exponents are identical — for instance, $\sqrt{3xy}$ and $5\sqrt{3xy}$ are like square roots because both share the radicand $3xy$ . In contrast, $\sqrt{2}$ and $\sqrt{7}$ are not like square roots because their radicands differ. Recognizing like square roots is essential because only like square roots can be combined through addition or subtraction — attempting to add square roots with different radicands is analogous to attempting to add unlike terms.

Updated 2026-04-21

Contributors are:

Who are from:

References

Learn Before

Related

Learn After