Solve 1/23-3sqrt{3+1}

$$\frac { 1 } { 2 } 3 - 3 \sqrt { 3 + 1 }$$

Evaluate

$$-\frac{9}{2}=-4.5$$

Solution Steps

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

$$\frac{3}{2}-3\sqrt{3+1}$$

Add 3 and 1 to get 4.

$$\frac{3}{2}-3\sqrt{4}$$

Calculate the square root of 4 and get 2.

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

Multiply 3 and 2 to get 6.

$$\frac{3}{2}-6$$

Convert 6 to fraction \frac{12}{2}.

$$\frac{3}{2}-\frac{12}{2}$$

Since \frac{3}{2} and \frac{12}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-12}{2}$$

Subtract 12 from 3 to get -9.

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

Factor

$$-\frac{9}{2} = -4\frac{1}{2} = -4.5$$