Solve (13/3)^2+(37/3)^2-10^2/2*frac{13{3}*37/3}-frac{sqrt{3}}{2}

$$\frac { ( \frac { 13 } { 3 } ) ^ { 2 } + ( \frac { 37 } { 3 } ) ^ { 2 } - 10 ^ { 2 } } { 2 \times \frac { 13 } { 3 } \times \frac { 37 } { 3 } } - \frac { \sqrt { 3 } } { 2 }$$

Evaluate

$$-\frac{\sqrt{3}}{2}+\frac{319}{481}\approx -0.202823741$$

Short Solution Steps

Calculate \frac{13}{3} to the power of 2 and get \frac{169}{9}.

$$\frac{\frac{169}{9}+\left(\frac{37}{3}\right)^{2}-10^{2}}{2\times \frac{13}{3}\times \frac{37}{3}}-\frac{\sqrt{3}}{2}$$

Calculate \frac{37}{3} to the power of 2 and get \frac{1369}{9}.

$$\frac{\frac{169}{9}+\frac{1369}{9}-10^{2}}{2\times \frac{13}{3}\times \frac{37}{3}}-\frac{\sqrt{3}}{2}$$

Since \frac{169}{9} and \frac{1369}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{169+1369}{9}-10^{2}}{2\times \frac{13}{3}\times \frac{37}{3}}-\frac{\sqrt{3}}{2}$$

Add 169 and 1369 to get 1538.

$$\frac{\frac{1538}{9}-10^{2}}{2\times \frac{13}{3}\times \frac{37}{3}}-\frac{\sqrt{3}}{2}$$

Calculate 10 to the power of 2 and get 100.

$$\frac{\frac{1538}{9}-100}{2\times \frac{13}{3}\times \frac{37}{3}}-\frac{\sqrt{3}}{2}$$

Convert 100 to fraction \frac{900}{9}.

$$\frac{\frac{1538}{9}-\frac{900}{9}}{2\times \frac{13}{3}\times \frac{37}{3}}-\frac{\sqrt{3}}{2}$$

Since \frac{1538}{9} and \frac{900}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1538-900}{9}}{2\times \frac{13}{3}\times \frac{37}{3}}-\frac{\sqrt{3}}{2}$$

Subtract 900 from 1538 to get 638.

$$\frac{\frac{638}{9}}{2\times \frac{13}{3}\times \frac{37}{3}}-\frac{\sqrt{3}}{2}$$

Express 2\times \frac{13}{3} as a single fraction.

$$\frac{\frac{638}{9}}{\frac{2\times 13}{3}\times \frac{37}{3}}-\frac{\sqrt{3}}{2}$$

Multiply 2 and 13 to get 26.

$$\frac{\frac{638}{9}}{\frac{26}{3}\times \frac{37}{3}}-\frac{\sqrt{3}}{2}$$

Multiply \frac{26}{3} times \frac{37}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{638}{9}}{\frac{26\times 37}{3\times 3}}-\frac{\sqrt{3}}{2}$$

Do the multiplications in the fraction \frac{26\times 37}{3\times 3}.

$$\frac{\frac{638}{9}}{\frac{962}{9}}-\frac{\sqrt{3}}{2}$$

Divide \frac{638}{9} by \frac{962}{9} by multiplying \frac{638}{9} by the reciprocal of \frac{962}{9}.

$$\frac{638}{9}\times \frac{9}{962}-\frac{\sqrt{3}}{2}$$

Multiply \frac{638}{9} times \frac{9}{962} by multiplying numerator times numerator and denominator times denominator.

$$\frac{638\times 9}{9\times 962}-\frac{\sqrt{3}}{2}$$

Cancel out 9 in both numerator and denominator.

$$\frac{638}{962}-\frac{\sqrt{3}}{2}$$

Reduce the fraction \frac{638}{962} to lowest terms by extracting and canceling out 2.

$$\frac{319}{481}-\frac{\sqrt{3}}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 481 and 2 is 962. Multiply \frac{319}{481} times \frac{2}{2}. Multiply \frac{\sqrt{3}}{2} times \frac{481}{481}.

$$\frac{319\times 2}{962}-\frac{481\sqrt{3}}{962}$$

Since \frac{319\times 2}{962} and \frac{481\sqrt{3}}{962} have the same denominator, subtract them by subtracting their numerators.

$$\frac{319\times 2-481\sqrt{3}}{962}$$

Do the multiplications in 319\times 2-481\sqrt{3}.

$$\frac{638-481\sqrt{3}}{962}$$

Factor

$$\frac{638 - 481 \sqrt{3}}{962} = -0.20282374058277544$$