Solve (frac{sqrt{14}}{2}+2-33/16)*(sqrt{14}div2+2-33div16)=

$$( \frac{ \sqrt{ 14 } }{ 2 } +2- \frac{ 33 }{ 16 } ) \times ( \sqrt{ 14 } \div 2+2-33 \div 16)=$$

Evaluate

$$-\frac{\sqrt{14}}{16}+\frac{897}{256}\approx 3.270052663$$

Short Solution Steps

Multiply \frac{\sqrt{14}}{2}+2-\frac{33}{16} and \frac{\sqrt{14}}{2}+2-\frac{33}{16} to get \left(\frac{\sqrt{14}}{2}+2-\frac{33}{16}\right)^{2}.

$$\left(\frac{\sqrt{14}}{2}+2-\frac{33}{16}\right)^{2}$$

Convert 2 to fraction \frac{32}{16}.

$$\left(\frac{\sqrt{14}}{2}+\frac{32}{16}-\frac{33}{16}\right)^{2}$$

Since \frac{32}{16} and \frac{33}{16} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{\sqrt{14}}{2}+\frac{32-33}{16}\right)^{2}$$

Subtract 33 from 32 to get -1.

$$\left(\frac{\sqrt{14}}{2}-\frac{1}{16}\right)^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 16 is 16. Multiply \frac{\sqrt{14}}{2} times \frac{8}{8}.

$$\left(\frac{8\sqrt{14}}{16}-\frac{1}{16}\right)^{2}$$

Since \frac{8\sqrt{14}}{16} and \frac{1}{16} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{8\sqrt{14}-1}{16}\right)^{2}$$

To raise \frac{8\sqrt{14}-1}{16} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(8\sqrt{14}-1\right)^{2}}{16^{2}}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(8\sqrt{14}-1\right)^{2}.

$$\frac{64\left(\sqrt{14}\right)^{2}-16\sqrt{14}+1}{16^{2}}$$

The square of \sqrt{14} is 14.

$$\frac{64\times 14-16\sqrt{14}+1}{16^{2}}$$

Multiply 64 and 14 to get 896.

$$\frac{896-16\sqrt{14}+1}{16^{2}}$$

Add 896 and 1 to get 897.

$$\frac{897-16\sqrt{14}}{16^{2}}$$

Calculate 16 to the power of 2 and get 256.

$$\frac{897-16\sqrt{14}}{256}$$

Factor

$$\frac{897 - 16 \sqrt{14}}{256} = 3.2700526633266285$$