Simplify square root of 50+3 cube root of 16-5 cube root of 54

$\sqrt{50} + 3 \sqrt[3]{16} - 5 \sqrt[3]{54}$

Simplify each term.

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$\sqrt{25 (2)} + 3 \sqrt[3]{16} - 5 \sqrt[3]{54}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 2} + 3 \sqrt[3]{16} - 5 \sqrt[3]{54}$

Pull terms out from under the radical.

$5 \sqrt{2} + 3 \sqrt[3]{16} - 5 \sqrt[3]{54}$

Rewrite $16$ as $2^{3} \cdot 2$ .

Factor $8$ out of $16$ .

$5 \sqrt{2} + 3 \sqrt[3]{8 (2)} - 5 \sqrt[3]{54}$

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

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

Pull terms out from under the radical.

$5 \sqrt{2} + 3 (2 \sqrt[3]{2}) - 5 \sqrt[3]{54}$

Multiply $2$ by $3$ .

$5 \sqrt{2} + 6 \sqrt[3]{2} - 5 \sqrt[3]{54}$

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

Factor $27$ out of $54$ .

$5 \sqrt{2} + 6 \sqrt[3]{2} - 5 \sqrt[3]{27 (2)}$

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

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

Pull terms out from under the radical.

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

Multiply $3$ by $- 5$ .

$5 \sqrt{2} + 6 \sqrt[3]{2} - 15 \sqrt[3]{2}$

Subtract $15 \sqrt[3]{2}$ from $6 \sqrt[3]{2}$ .

$5 \sqrt{2} - 9 \sqrt[3]{2}$

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{2} - 9 \sqrt[3]{2}$

Decimal Form:

$- 4.26822163 \dots$