Solve 2sqrt{3}-3-(1/2sqrt{27}-sqrt{9})

$$2 \sqrt { 3 } - 3 - ( \frac { 1 } { 2 } \sqrt { 27 } - \sqrt { 9 } )$$

Evaluate

$$\frac{\sqrt{3}}{2}\approx 0.866025404$$

Solution Steps

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$2\sqrt{3}-3-\left(\frac{1}{2}\times 3\sqrt{3}-\sqrt{9}\right)$$

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

$$2\sqrt{3}-3-\left(\frac{3}{2}\sqrt{3}-\sqrt{9}\right)$$

Calculate the square root of 9 and get 3.

$$2\sqrt{3}-3-\left(\frac{3}{2}\sqrt{3}-3\right)$$

To find the opposite of \frac{3}{2}\sqrt{3}-3, find the opposite of each term.

$$2\sqrt{3}-3-\frac{3}{2}\sqrt{3}-\left(-3\right)$$

Combine 2\sqrt{3} and -\frac{3}{2}\sqrt{3} to get \frac{1}{2}\sqrt{3}.

$$\frac{1}{2}\sqrt{3}-3-\left(-3\right)$$

The opposite of -3 is 3.

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

Add -3 and 3 to get 0.

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