Simplify fourth root of 32+ fourth root of 48

$\sqrt[4]{32} + \sqrt[4]{48}$

Step 1

Rewrite $32$ as $2^{4} \cdot 2$ .

Factor $16$ out of $32$ .

$\sqrt[4]{16 (2)} + \sqrt[4]{48}$

Rewrite $16$ as $2^{4}$ .

$\sqrt[4]{2^{4} \cdot 2} + \sqrt[4]{48}$

$\sqrt[4]{2^{4} \cdot 2} + \sqrt[4]{48}$

Step 2

Pull terms out from under the radical.

$2 \sqrt[4]{2} + \sqrt[4]{48}$

Step 3

Rewrite $48$ as $2^{4} \cdot 3$ .

Factor $16$ out of $48$ .

$2 \sqrt[4]{2} + \sqrt[4]{16 (3)}$

Rewrite $16$ as $2^{4}$ .

$2 \sqrt[4]{2} + \sqrt[4]{2^{4} \cdot 3}$

$2 \sqrt[4]{2} + \sqrt[4]{2^{4} \cdot 3}$

Step 4

Pull terms out from under the radical.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$5.01056225 \dots$

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