Solve (frac{sqrt{14}}{2}+2)^2

$$( \frac { \sqrt { 14 } } { 2 } + 2 ) ^ { 2 }$$

Evaluate

$$2\sqrt{14}+\frac{15}{2}\approx 14.983314774$$

Short Solution Steps

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

$$\left(\frac{\sqrt{14}}{2}+\frac{2\times 2}{2}\right)^{2}$$

Since \frac{\sqrt{14}}{2} and \frac{2\times 2}{2} have the same denominator, add them by adding their numerators.

$$\left(\frac{\sqrt{14}+2\times 2}{2}\right)^{2}$$

Do the multiplications in \sqrt{14}+2\times 2.

$$\left(\frac{\sqrt{14}+4}{2}\right)^{2}$$

To raise \frac{\sqrt{14}+4}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(\sqrt{14}+4\right)^{2}}{2^{2}}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{14}+4\right)^{2}.

$$\frac{\left(\sqrt{14}\right)^{2}+8\sqrt{14}+16}{2^{2}}$$

The square of \sqrt{14} is 14.

$$\frac{14+8\sqrt{14}+16}{2^{2}}$$

Add 14 and 16 to get 30.

$$\frac{30+8\sqrt{14}}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{30+8\sqrt{14}}{4}$$

Expand

$$2 \sqrt{14} + \frac{15}{2} = 14.983314774$$

Short Solution Steps

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

$$\left(\frac{\sqrt{14}}{2}+\frac{2\times 2}{2}\right)^{2}$$

Since \frac{\sqrt{14}}{2} and \frac{2\times 2}{2} have the same denominator, add them by adding their numerators.

$$\left(\frac{\sqrt{14}+2\times 2}{2}\right)^{2}$$

Do the multiplications in \sqrt{14}+2\times 2.

$$\left(\frac{\sqrt{14}+4}{2}\right)^{2}$$

To raise \frac{\sqrt{14}+4}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(\sqrt{14}+4\right)^{2}}{2^{2}}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{14}+4\right)^{2}.

$$\frac{\left(\sqrt{14}\right)^{2}+8\sqrt{14}+16}{2^{2}}$$

The square of \sqrt{14} is 14.

$$\frac{14+8\sqrt{14}+16}{2^{2}}$$

Add 14 and 16 to get 30.

$$\frac{30+8\sqrt{14}}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{30+8\sqrt{14}}{4}$$