Solve 5*22*15*15/42+frac{sqrt{3}}{4}*15*15

$$\frac { 5 \times 22 \times 15 \times 15 } { 42 } + \frac { \sqrt { 3 } } { 4 } \times 15 \times 15$$

Evaluate

$$\frac{225\sqrt{3}}{4}+\frac{4125}{7}\approx 686.713572211$$

Short Solution Steps

Multiply 5 and 22 to get 110.

$$\frac{110\times 15\times 15}{42}+15\times 15\times \frac{\sqrt{3}}{4}$$

Multiply 110 and 15 to get 1650.

$$\frac{1650\times 15}{42}+15\times 15\times \frac{\sqrt{3}}{4}$$

Multiply 1650 and 15 to get 24750.

$$\frac{24750}{42}+15\times 15\times \frac{\sqrt{3}}{4}$$

Reduce the fraction \frac{24750}{42} to lowest terms by extracting and canceling out 6.

$$\frac{4125}{7}+15\times 15\times \frac{\sqrt{3}}{4}$$

Multiply 15 and 15 to get 225.

$$\frac{4125}{7}+225\times \frac{\sqrt{3}}{4}$$

Express 225\times \frac{\sqrt{3}}{4} as a single fraction.

$$\frac{4125}{7}+\frac{225\sqrt{3}}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7 and 4 is 28. Multiply \frac{4125}{7} times \frac{4}{4}. Multiply \frac{225\sqrt{3}}{4} times \frac{7}{7}.

$$\frac{4125\times 4}{28}+\frac{7\times 225\sqrt{3}}{28}$$

Since \frac{4125\times 4}{28} and \frac{7\times 225\sqrt{3}}{28} have the same denominator, add them by adding their numerators.

$$\frac{4125\times 4+7\times 225\sqrt{3}}{28}$$

Do the multiplications in 4125\times 4+7\times 225\sqrt{3}.

$$\frac{16500+1575\sqrt{3}}{28}$$

Factor

$$\frac{75 {(21 \sqrt{3} + 220)}}{28} = 686.7135722114637$$