Solve sqrt{2*36+576div8}+{(sqrt{9}-sqrt{4})^2-[7+(8-2)-(5-4)]+6}

$$\sqrt { 2 \cdot 36 + 576 \div 8 } + \{ ( \sqrt { 9 } - \sqrt { 4 } ) ^ { 2 } - [ 7 + ( 8 - 2 ) - ( 5 - 4 ) ] + 6 \}$$

Evaluate

$$7$$

Solution Steps

Multiply 2 and 36 to get 72.

$$\sqrt{72+\frac{576}{8}}+\left(\sqrt{9}-\sqrt{4}\right)^{2}-\left(7+8-2-\left(5-4\right)\right)+6$$

Divide 576 by 8 to get 72.

$$\sqrt{72+72}+\left(\sqrt{9}-\sqrt{4}\right)^{2}-\left(7+8-2-\left(5-4\right)\right)+6$$

Add 72 and 72 to get 144.

$$\sqrt{144}+\left(\sqrt{9}-\sqrt{4}\right)^{2}-\left(7+8-2-\left(5-4\right)\right)+6$$

Calculate the square root of 144 and get 12.

$$12+\left(\sqrt{9}-\sqrt{4}\right)^{2}-\left(7+8-2-\left(5-4\right)\right)+6$$

Calculate the square root of 9 and get 3.

$$12+\left(3-\sqrt{4}\right)^{2}-\left(7+8-2-\left(5-4\right)\right)+6$$

Calculate the square root of 4 and get 2.

$$12+\left(3-2\right)^{2}-\left(7+8-2-\left(5-4\right)\right)+6$$

Subtract 2 from 3 to get 1.

$$12+1^{2}-\left(7+8-2-\left(5-4\right)\right)+6$$

Calculate 1 to the power of 2 and get 1.

$$12+1-\left(7+8-2-\left(5-4\right)\right)+6$$

Add 7 and 8 to get 15.

$$12+1-\left(15-2-\left(5-4\right)\right)+6$$

Subtract 2 from 15 to get 13.

$$12+1-\left(13-\left(5-4\right)\right)+6$$

Subtract 4 from 5 to get 1.

$$12+1-\left(13-1\right)+6$$

Subtract 1 from 13 to get 12.

$$12+1-12+6$$

Subtract 12 from 1 to get -11.

$$12-11+6$$

Subtract 11 from 12 to get 1.

$$1+6$$

Add 1 and 6 to get 7.

$$7$$

Factor

$$7$$