1Cademy - Simplifying $$8\sqrt{2} - 9\sqrt{2}$$, $$4\sqrt[3]{x} + 7\sqrt[3]{x}$$, and $$3\sqrt[4]{x}

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Adding and Subtracting Like Radicals

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Simplifying $8\sqrt{2} - 9\sqrt{2}$ , $4\sqrt[3]{x} + 7\sqrt[3]{x}$ , and $3\sqrt[4]{x} - 5\sqrt[4]{y}$

Simplify expressions containing radicals by first determining if they are like terms. ⓐ $8\sqrt{2} - 9\sqrt{2} = -\sqrt{2}$ : These square roots share the radicand $2$ , making them like radicals. Subtracting the coefficients ( $8 - 9 = -1$ ) gives $-\sqrt{2}$ . ⓑ $4\sqrt[3]{x} + 7\sqrt[3]{x} = 11\sqrt[3]{x}$ : These cube roots share the radicand $x$ . Adding their coefficients ( $4 + 7 = 11$ ) results in $11\sqrt[3]{x}$ . ⓒ $3\sqrt[4]{x} - 5\sqrt[4]{y}$ : While both have an index of $4$ , their differing radicands ( $x$ and $y$ ) mean they are not like radicals and cannot be combined. The expression $3\sqrt[4]{x} - 5\sqrt[4]{y}$ is already simplified.

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Updated 2026-06-03

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OpenStax Intermediate Algebra

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