Simplify cube root of 24-2 fourth root of 112+3 fourth root of 7

$\sqrt[3]{24} - 2 \sqrt[4]{112} + 3 \sqrt[4]{7}$

Simplify each term.

Rewrite $24$ as $2^{3} \cdot 3$ .

Factor $8$ out of $24$ .

$\sqrt[3]{8 (3)} - 2 \sqrt[4]{112} + 3 \sqrt[4]{7}$

Rewrite $8$ as $2^{3}$ .

$\sqrt[3]{2^{3} \cdot 3} - 2 \sqrt[4]{112} + 3 \sqrt[4]{7}$

Pull terms out from under the radical.

$2 \sqrt[3]{3} - 2 \sqrt[4]{112} + 3 \sqrt[4]{7}$

Rewrite $112$ as $2^{4} \cdot 7$ .

Factor $16$ out of $112$ .

$2 \sqrt[3]{3} - 2 \sqrt[4]{16 (7)} + 3 \sqrt[4]{7}$

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

$2 \sqrt[3]{3} - 2 \sqrt[4]{2^{4} \cdot 7} + 3 \sqrt[4]{7}$

Pull terms out from under the radical.

$2 \sqrt[3]{3} - 2 (2 \sqrt[4]{7}) + 3 \sqrt[4]{7}$

Multiply $2$ by $- 2$ .

$2 \sqrt[3]{3} - 4 \sqrt[4]{7} + 3 \sqrt[4]{7}$

Add $- 4 \sqrt[4]{7}$ and $3 \sqrt[4]{7}$ .

$2 \sqrt[3]{3} - \sqrt[4]{7}$

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt[3]{3} - \sqrt[4]{7}$

Decimal Form:

$1.25792257 \dots$