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

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

Evaluate

$$\sqrt{3}-\frac{1}{4}\approx 1.482050808$$

Short Solution Steps

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

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

Since \frac{\sqrt{3}}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

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

To raise \frac{\sqrt{3}+2}{2} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

Since \frac{\left(\sqrt{3}+2\right)^{2}}{2^{2}} and \frac{2\times 2^{2}}{2^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

$$\frac{\left(\sqrt{3}\right)^{2}+4\sqrt{3}+4-8}{2^{2}}$$

Do the calculations in \left(\sqrt{3}\right)^{2}+4\sqrt{3}+4-8.

$$\frac{-1+4\sqrt{3}}{2^{2}}$$

Expand 2^{2}.

$$\frac{-1+4\sqrt{3}}{4}$$

Expand

$$\sqrt{3} - \frac{1}{4} = 1.482050808$$

Short Solution Steps

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

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

Since \frac{\sqrt{3}}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

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

To raise \frac{\sqrt{3}+2}{2} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

Since \frac{\left(\sqrt{3}+2\right)^{2}}{2^{2}} and \frac{2\times 2^{2}}{2^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

$$\frac{\left(\sqrt{3}\right)^{2}+4\sqrt{3}+4-8}{2^{2}}$$

Do the calculations in \left(\sqrt{3}\right)^{2}+4\sqrt{3}+4-8.

$$\frac{-1+4\sqrt{3}}{2^{2}}$$

Expand 2^{2}.

$$\frac{-1+4\sqrt{3}}{4}$$