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

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

Evaluate

$$\frac{7-2\sqrt{3}}{3}\approx 1.178632795$$

Short Solution Steps

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

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

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

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3^{2}}{3^{2}}.

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

Since \frac{\left(\sqrt{3}-3\right)^{2}}{3^{2}} and \frac{3^{2}}{3^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(\sqrt{3}-3\right)^{2}+3^{2}.

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

Do the calculations in \left(\sqrt{3}\right)^{2}-6\sqrt{3}+9+3^{2}.

$$\frac{21-6\sqrt{3}}{3^{2}}$$

Expand 3^{2}.

$$\frac{21-6\sqrt{3}}{9}$$

Expand

$$\frac{7 - 2 \sqrt{3}}{3} = 1.1786327949540818$$

Short Solution Steps

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

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

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

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3^{2}}{3^{2}}.

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

Since \frac{\left(\sqrt{3}-3\right)^{2}}{3^{2}} and \frac{3^{2}}{3^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(\sqrt{3}-3\right)^{2}+3^{2}.

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

Do the calculations in \left(\sqrt{3}\right)^{2}-6\sqrt{3}+9+3^{2}.

$$\frac{21-6\sqrt{3}}{3^{2}}$$

Expand 3^{2}.

$$\frac{21-6\sqrt{3}}{9}$$