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

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Adding and Subtracting Like Square Roots

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Simplifying $\sqrt[3]{4x} + \sqrt[3]{4x}$ and $4\sqrt[4]{8} - 2\sqrt[4]{8}$

Simplify two expressions involving higher roots that are already like radicals.

ⓐ $\sqrt[3]{4x} + \sqrt[3]{4x} = 2\sqrt[3]{4x}$ :

Both terms are cube roots with the same radicand $4x$ , so they are like radicals. Each term has an implicit coefficient of $1$ . Add the coefficients: $1 + 1 = 2$ .

$\sqrt[3]{4x} + \sqrt[3]{4x} = 2\sqrt[3]{4x}$

ⓑ $4\sqrt[4]{8} - 2\sqrt[4]{8} = 2\sqrt[4]{8}$ :

Both terms are fourth roots with the same radicand $8$ , so they are like radicals. Subtract the coefficients: $4 - 2 = 2$ .

$4\sqrt[4]{8} - 2\sqrt[4]{8} = 2\sqrt[4]{8}$

In both parts, the radicals share the same index and radicand, so only the coefficients are combined while the radical factor remains unchanged — the same approach used when combining like square roots or like terms in algebra.

Updated 2026-05-14

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