Simplify cube root of 250+ cube root of 54+ square root of 72

$\sqrt[3]{250} + \sqrt[3]{54} + \sqrt{72}$

Simplify each term.

Rewrite $250$ as $5^{3} \cdot 2$ .

Factor $125$ out of $250$ .

$\sqrt[3]{125 (2)} + \sqrt[3]{54} + \sqrt{72}$

Rewrite $125$ as $5^{3}$ .

$\sqrt[3]{5^{3} \cdot 2} + \sqrt[3]{54} + \sqrt{72}$

Pull terms out from under the radical.

$5 \sqrt[3]{2} + \sqrt[3]{54} + \sqrt{72}$

Rewrite $54$ as $3^{3} \cdot 2$ .

Factor $27$ out of $54$ .

$5 \sqrt[3]{2} + \sqrt[3]{27 (2)} + \sqrt{72}$

Rewrite $27$ as $3^{3}$ .

$5 \sqrt[3]{2} + \sqrt[3]{3^{3} \cdot 2} + \sqrt{72}$

Pull terms out from under the radical.

$5 \sqrt[3]{2} + 3 \sqrt[3]{2} + \sqrt{72}$

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$5 \sqrt[3]{2} + 3 \sqrt[3]{2} + \sqrt{36 (2)}$

Rewrite $36$ as $6^{2}$ .

$5 \sqrt[3]{2} + 3 \sqrt[3]{2} + \sqrt{6^{2} \cdot 2}$

Pull terms out from under the radical.

$5 \sqrt[3]{2} + 3 \sqrt[3]{2} + 6 \sqrt{2}$

Add $5 \sqrt[3]{2}$ and $3 \sqrt[3]{2}$ .

$8 \sqrt[3]{2} + 6 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$8 \sqrt[3]{2} + 6 \sqrt{2}$

Decimal Form:

$18.56464977 \dots$