1Cademy - Simplifying $$2\sqrt{6} - 6\sqrt{6} + 3\sqrt{3}$$

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Adding and Subtracting Like Square Roots

Example

Simplifying $2\sqrt{6} - 6\sqrt{6} + 3\sqrt{3}$

Simplify the expression $2\sqrt{6} - 6\sqrt{6} + 3\sqrt{3}$ , which contains a mixture of like and unlike square roots.

The first two terms, $2\sqrt{6}$ and $-6\sqrt{6}$ , share the radicand $6$ and are therefore like square roots. The third term, $3\sqrt{3}$ , has a different radicand ( $3$ ) and cannot be combined with the others. Subtract the coefficients of the like radicals: $2 - 6 = -4$ .

$2\sqrt{6} - 6\sqrt{6} + 3\sqrt{3} = -4\sqrt{6} + 3\sqrt{3}$

This example illustrates that when an expression contains both like and unlike square roots, only the like ones are combined. The unlike term is carried through unchanged — exactly as one would do with a mixed expression such as $2a - 6a + 3b = -4a + 3b$ in algebra.

Updated 2026-04-21

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OpenStax Elementary Algebra

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