1Cademy - Simplifying $$ 5\sqrt[3]{y} + 4\sqrt[3]{y} $$ and $$ 7\sqrt[4]{x}

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Adding and Subtracting Like Radicals

Example

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

Simplify the following higher-order radical expressions by determining if they are like radicals:

ⓐ $5\sqrt[3]{y} + 4\sqrt[3]{y}$ : These terms are like radicals because they share the same index ( $3$ ) and radicand ( $y$ ). Adding their coefficients ( $5 + 4 = 9$ ) while leaving the radical factor unchanged yields $9\sqrt[3]{y}$ .

ⓑ $7\sqrt[4]{x} - 2\sqrt[4]{y}$ : Although both terms share an index of $4$ , their radicands ( $x$ and $y$ ) are different. Consequently, they are not like radicals and cannot be combined. The expression remains $7\sqrt[4]{x} - 2\sqrt[4]{y}$ .