Solve 314*15*15*60div360-225*frac{sqrt{3}}{4}*1/720

$$314 \times 15 \times 15 \times 60 \div 360-225 \times \frac{ \sqrt{ 3 } }{ 4 } \times \frac{ 1 }{ 720 }$$

Evaluate

$$-\frac{5\sqrt{3}}{64}+11775\approx 11774.864683531$$

Short Solution Steps

Multiply 314 and 15 to get 4710.

$$\frac{4710\times 15\times 60}{360}-225\times \frac{\sqrt{3}}{4}\times \frac{1}{720}$$

Multiply 4710 and 15 to get 70650.

$$\frac{70650\times 60}{360}-225\times \frac{\sqrt{3}}{4}\times \frac{1}{720}$$

Multiply 70650 and 60 to get 4239000.

$$\frac{4239000}{360}-225\times \frac{\sqrt{3}}{4}\times \frac{1}{720}$$

Divide 4239000 by 360 to get 11775.

$$11775-225\times \frac{\sqrt{3}}{4}\times \frac{1}{720}$$

Multiply 225 and \frac{1}{720} to get \frac{225}{720}.

$$11775-\frac{225}{720}\times \frac{\sqrt{3}}{4}$$

Reduce the fraction \frac{225}{720} to lowest terms by extracting and canceling out 45.

$$11775-\frac{5}{16}\times \frac{\sqrt{3}}{4}$$

Multiply \frac{5}{16} times \frac{\sqrt{3}}{4} by multiplying numerator times numerator and denominator times denominator.

$$11775-\frac{5\sqrt{3}}{16\times 4}$$

Multiply 16 and 4 to get 64.

$$11775-\frac{5\sqrt{3}}{64}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 11775 times \frac{64}{64}.

$$\frac{11775\times 64}{64}-\frac{5\sqrt{3}}{64}$$

Since \frac{11775\times 64}{64} and \frac{5\sqrt{3}}{64} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11775\times 64-5\sqrt{3}}{64}$$

Do the multiplications in 11775\times 64-5\sqrt{3}.

$$\frac{753600-5\sqrt{3}}{64}$$

Factor

$$\frac{5 {(150720 - \sqrt{3})}}{64} = 11774.864683530659$$