Solve sqrt{[14+3*8-(2^2+2^3+5*2^2)+9*8]:2}

$$\sqrt { [ 14 + 3 \times 8 - ( 2 ^ { 2 } + 2 ^ { 3 } + 5 \times 2 ^ { 2 } ) + 9 \times 8 ] : 2 }$$

Evaluate

$$\sqrt{39}\approx 6.244997998$$

Solution Steps

Multiply 3 and 8 to get 24.

$$\sqrt{\frac{14+24-\left(2^{2}+2^{3}+5\times 2^{2}\right)+9\times 8}{2}}$$

Add 14 and 24 to get 38.

$$\sqrt{\frac{38-\left(2^{2}+2^{3}+5\times 2^{2}\right)+9\times 8}{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{\frac{38-\left(4+2^{3}+5\times 2^{2}\right)+9\times 8}{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\sqrt{\frac{38-\left(4+8+5\times 2^{2}\right)+9\times 8}{2}}$$

Add 4 and 8 to get 12.

$$\sqrt{\frac{38-\left(12+5\times 2^{2}\right)+9\times 8}{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{\frac{38-\left(12+5\times 4\right)+9\times 8}{2}}$$

Multiply 5 and 4 to get 20.

$$\sqrt{\frac{38-\left(12+20\right)+9\times 8}{2}}$$

Add 12 and 20 to get 32.

$$\sqrt{\frac{38-32+9\times 8}{2}}$$

Subtract 32 from 38 to get 6.

$$\sqrt{\frac{6+9\times 8}{2}}$$

Multiply 9 and 8 to get 72.

$$\sqrt{\frac{6+72}{2}}$$

Add 6 and 72 to get 78.

$$\sqrt{\frac{78}{2}}$$

Divide 78 by 2 to get 39.

$$\sqrt{39}$$