Solve 2/sqrt{3}*0.5*(2.7+9.8)div0.25div0.5

$$\frac{ 2 }{ \sqrt{ 3 } } \times 0.5 \times (2.7+9.8) \div 0.25 \div 0.5$$

Evaluate

$$\frac{100\sqrt{3}}{3}\approx 57.735026919$$

Solution Steps

Express \frac{\frac{0.5\times \frac{2}{\sqrt{3}}\left(2.7+9.8\right)}{0.25}}{0.5} as a single fraction.

$$\frac{0.5\times \frac{2}{\sqrt{3}}\left(2.7+9.8\right)}{0.25\times 0.5}$$

Rationalize the denominator of \frac{2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{0.5\times \frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\left(2.7+9.8\right)}{0.25\times 0.5}$$

The square of \sqrt{3} is 3.

$$\frac{0.5\times \frac{2\sqrt{3}}{3}\left(2.7+9.8\right)}{0.25\times 0.5}$$

Add 2.7 and 9.8 to get 12.5.

$$\frac{0.5\times \frac{2\sqrt{3}}{3}\times 12.5}{0.25\times 0.5}$$

Multiply 0.5 and 12.5 to get 6.25.

$$\frac{6.25\times \frac{2\sqrt{3}}{3}}{0.25\times 0.5}$$

Multiply 0.25 and 0.5 to get 0.125.

$$\frac{6.25\times \frac{2\sqrt{3}}{3}}{0.125}$$

Divide 6.25\times \frac{2\sqrt{3}}{3} by 0.125 to get 50\times \frac{2\sqrt{3}}{3}.

$$50\times \frac{2\sqrt{3}}{3}$$

Express 50\times \frac{2\sqrt{3}}{3} as a single fraction.

$$\frac{50\times 2\sqrt{3}}{3}$$

Multiply 50 and 2 to get 100.

$$\frac{100\sqrt{3}}{3}$$