Solve 3.14*15*15*60div360-225*frac{sqrt{3}}{4}*1/720

$$3.14 \times 15 \times 15 \times 60 \div 360-225 \times \frac{ \sqrt{ 3 } }{ 4 } \times \frac{ 1 }{ 720 }$$

Evaluate

$$-\frac{5\sqrt{3}}{64}+117.75\approx 117.614683531$$

Short Solution Steps

Multiply 3.14 and 15 to get 47.1.

$$\frac{47.1\times 15\times 60}{360}-225\times \frac{\sqrt{3}}{4}\times \frac{1}{720}$$

Multiply 47.1 and 15 to get 706.5.

$$\frac{706.5\times 60}{360}-225\times \frac{\sqrt{3}}{4}\times \frac{1}{720}$$

Multiply 706.5 and 60 to get 42390.

$$\frac{42390}{360}-225\times \frac{\sqrt{3}}{4}\times \frac{1}{720}$$

Reduce the fraction \frac{42390}{360} to lowest terms by extracting and canceling out 90.

$$\frac{471}{4}-225\times \frac{\sqrt{3}}{4}\times \frac{1}{720}$$

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

$$\frac{471}{4}-\frac{225}{720}\times \frac{\sqrt{3}}{4}$$

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

$$\frac{471}{4}-\frac{5}{16}\times \frac{\sqrt{3}}{4}$$

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

$$\frac{471}{4}-\frac{5\sqrt{3}}{16\times 4}$$

Multiply 16 and 4 to get 64.

$$\frac{471}{4}-\frac{5\sqrt{3}}{64}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 64 is 64. Multiply \frac{471}{4} times \frac{16}{16}.

$$\frac{471\times 16}{64}-\frac{5\sqrt{3}}{64}$$

Since \frac{471\times 16}{64} and \frac{5\sqrt{3}}{64} have the same denominator, subtract them by subtracting their numerators.

$$\frac{471\times 16-5\sqrt{3}}{64}$$

Do the multiplications in 471\times 16-5\sqrt{3}.

$$\frac{7536-5\sqrt{3}}{64}$$

Factor

$$\frac{7536 - 5 \sqrt{3}}{64} = 117.61468353065868$$