Simplify 2 fourth root of 48+3 fourth root of 243

$2 \sqrt[4]{48} + 3 \sqrt[4]{243}$

Step 1

Simplify each term.

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

Factor $16$ out of $48$ .

$2 \sqrt[4]{16 (3)} + 3 \sqrt[4]{243}$

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

$2 \sqrt[4]{2^{4} \cdot 3} + 3 \sqrt[4]{243}$

$2 \sqrt[4]{2^{4} \cdot 3} + 3 \sqrt[4]{243}$

Pull terms out from under the radical.

$2 (2 \sqrt[4]{3}) + 3 \sqrt[4]{243}$

Multiply $2$ by $2$ .

$4 \sqrt[4]{3} + 3 \sqrt[4]{243}$

Rewrite $243$ as $3^{4} \cdot 3$ .

Factor $81$ out of $243$ .

$4 \sqrt[4]{3} + 3 \sqrt[4]{81 (3)}$

Rewrite $81$ as $3^{4}$ .

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

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

Pull terms out from under the radical.

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

Multiply $3$ by $3$ .

$4 \sqrt[4]{3} + 9 \sqrt[4]{3}$

$4 \sqrt[4]{3} + 9 \sqrt[4]{3}$

Step 2

Add $4 \sqrt[4]{3}$ and $9 \sqrt[4]{3}$ .

$13 \sqrt[4]{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$13 \sqrt[4]{3}$

Decimal Form:

$17.10896216 \dots$

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