Solve (-frac{sqrt{3}}{3}+1)^2=

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

Evaluate

$$\frac{4-2\sqrt{3}}{3}\approx 0.178632795$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3}{3}.

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

Since -\frac{\sqrt{3}}{3} and \frac{3}{3} have the same denominator, add them by adding their numerators.

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

To raise \frac{-\sqrt{3}+3}{3} to a power, raise both numerator and denominator to the power and then divide.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-\sqrt{3}+3\right)^{2}.

$$\frac{\left(\sqrt{3}\right)^{2}-6\sqrt{3}+9}{3^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{3-6\sqrt{3}+9}{3^{2}}$$

Add 3 and 9 to get 12.

$$\frac{12-6\sqrt{3}}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{12-6\sqrt{3}}{9}$$

Expand

$$\frac{4 - 2 \sqrt{3}}{3} = 0.17863279495408188$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3}{3}.

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

Since -\frac{\sqrt{3}}{3} and \frac{3}{3} have the same denominator, add them by adding their numerators.

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

To raise \frac{-\sqrt{3}+3}{3} to a power, raise both numerator and denominator to the power and then divide.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-\sqrt{3}+3\right)^{2}.

$$\frac{\left(\sqrt{3}\right)^{2}-6\sqrt{3}+9}{3^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{3-6\sqrt{3}+9}{3^{2}}$$

Add 3 and 9 to get 12.

$$\frac{12-6\sqrt{3}}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{12-6\sqrt{3}}{9}$$