Solve (2)(-3)^2-|-1/2|+2^2-sqrt{9}

$$( 2 ) ( - 3 ) ^ { 2 } - | - \frac { 1 } { 2 } | + 2 ^ { 2 } - \sqrt { 9 }$$

Evaluate

$$\frac{37}{2}=18.5$$

Solution Steps

Calculate -3 to the power of 2 and get 9.

$$2\times 9-|-\frac{1}{2}|+2^{2}-\sqrt{9}$$

Multiply 2 and 9 to get 18.

$$18-|-\frac{1}{2}|+2^{2}-\sqrt{9}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{1}{2} is \frac{1}{2}.

$$18-\frac{1}{2}+2^{2}-\sqrt{9}$$

Convert 18 to fraction \frac{36}{2}.

$$\frac{36}{2}-\frac{1}{2}+2^{2}-\sqrt{9}$$

Since \frac{36}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{36-1}{2}+2^{2}-\sqrt{9}$$

Subtract 1 from 36 to get 35.

$$\frac{35}{2}+2^{2}-\sqrt{9}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{35}{2}+4-\sqrt{9}$$

Convert 4 to fraction \frac{8}{2}.

$$\frac{35}{2}+\frac{8}{2}-\sqrt{9}$$

Since \frac{35}{2} and \frac{8}{2} have the same denominator, add them by adding their numerators.

$$\frac{35+8}{2}-\sqrt{9}$$

Add 35 and 8 to get 43.

$$\frac{43}{2}-\sqrt{9}$$

Calculate the square root of 9 and get 3.

$$\frac{43}{2}-3$$

Convert 3 to fraction \frac{6}{2}.

$$\frac{43}{2}-\frac{6}{2}$$

Since \frac{43}{2} and \frac{6}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{43-6}{2}$$

Subtract 6 from 43 to get 37.

$$\frac{37}{2}$$

Factor

$$\frac{37}{2} = 18\frac{1}{2} = 18.5$$