Evaluate cube root of 64+(2+1)^2- square root of 9+(10-7)^3

$\sqrt[3]{64} + {(2 + 1)}^{2} - \sqrt{9} + {(10 - 7)}^{3}$

Step 1

Simplify each term.

Rewrite $64$ as $4^{3}$ .

$\sqrt[3]{4^{3}} + {(2 + 1)}^{2} - \sqrt{9} + {(10 - 7)}^{3}$

Pull terms out from under the radical, assuming real numbers.

$4 + {(2 + 1)}^{2} - \sqrt{9} + {(10 - 7)}^{3}$

Add $2$ and $1$ .

$4 + 3^{2} - \sqrt{9} + {(10 - 7)}^{3}$

Raise $3$ to the power of $2$ .

$4 + 9 - \sqrt{9} + {(10 - 7)}^{3}$

Rewrite $9$ as $3^{2}$ .

$4 + 9 - \sqrt{3^{2}} + {(10 - 7)}^{3}$

Pull terms out from under the radical, assuming positive real numbers.

$4 + 9 - 1 \cdot 3 + {(10 - 7)}^{3}$

Multiply $- 1$ by $3$ .

$4 + 9 - 3 + {(10 - 7)}^{3}$

Subtract $7$ from $10$ .

$4 + 9 - 3 + 3^{3}$

Raise $3$ to the power of $3$ .

$4 + 9 - 3 + 27$

Step 2

Simplify by adding and subtracting.

Add $4$ and $9$ .

$13 - 3 + 27$

Subtract $3$ from $13$ .

$10 + 27$

Add $10$ and $27$ .

$37$