1Cademy - Simplifying $$5\sqrt{3} - 9\sqrt{3}$$, $$5\sqrt[3]{y} + 3\sqrt[3]{y}$$, and $$5\sqrt[4]{m}

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Adding and Subtracting Like Radicals

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Simplifying $5\sqrt{3} - 9\sqrt{3}$ , $5\sqrt[3]{y} + 3\sqrt[3]{y}$ , and $5\sqrt[4]{m} - 2\sqrt[3]{m}$

Determine whether radicals can be combined by checking their indices and radicands. ⓐ $5\sqrt{3} - 9\sqrt{3} = -4\sqrt{3}$ : Both terms share an index of $2$ and a radicand of $3$ . Subtracting the coefficients ( $5 - 9 = -4$ ) produces $-4\sqrt{3}$ . ⓑ $5\sqrt[3]{y} + 3\sqrt[3]{y} = 8\sqrt[3]{y}$ : These terms are like radicals because they share the index $3$ and radicand $y$ . Combining their coefficients yields $8\sqrt[3]{y}$ . ⓒ $5\sqrt[4]{m} - 2\sqrt[3]{m}$ : Although both terms have a radicand of $m$ , their distinct indices ( $4$ and $3$ ) mean they are not like radicals. The expression $5\sqrt[4]{m} - 2\sqrt[3]{m}$ cannot be simplified further.

Updated 2026-05-26

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OpenStax Intermediate Algebra

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