Solve 2*250/0.05^2*1.256610^-6frac{8*1.58*154{sqrt{12}5*0.2}}

$$\frac{ 2 \cdot 250 }{ { 0.05 }^{ 2 } \times 1.2566 { 10 }^{ -6 } \frac{ 8 \cdot 1.58 \cdot 154 }{ \sqrt{ 12 } 5 \cdot 0.2 } }$$

Evaluate

$$\frac{6250000000000000\sqrt{3}}{38219489}\approx 283240771.41129446$$

Solution Steps

Multiply 2 and 250 to get 500.

$$\frac{500}{1.2566\times 0.05^{2}\times 10^{-6}\times \frac{8\times 1.58\times 154}{0.2\times 5\sqrt{12}}}$$

Calculate 0.05 to the power of 2 and get 0.0025.

$$\frac{500}{1.2566\times 0.0025\times 10^{-6}\times \frac{8\times 1.58\times 154}{0.2\times 5\sqrt{12}}}$$

Multiply 1.2566 and 0.0025 to get 0.0031415.

$$\frac{500}{0.0031415\times 10^{-6}\times \frac{8\times 1.58\times 154}{0.2\times 5\sqrt{12}}}$$

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$\frac{500}{0.0031415\times \frac{1}{1000000}\times \frac{8\times 1.58\times 154}{0.2\times 5\sqrt{12}}}$$

Multiply 0.0031415 and \frac{1}{1000000} to get \frac{6283}{2000000000000}.

$$\frac{500}{\frac{6283}{2000000000000}\times \frac{8\times 1.58\times 154}{0.2\times 5\sqrt{12}}}$$

Multiply 8 and 1.58 to get 12.64.

$$\frac{500}{\frac{6283}{2000000000000}\times \frac{12.64\times 154}{0.2\times 5\sqrt{12}}}$$

Multiply 12.64 and 154 to get 1946.56.

$$\frac{500}{\frac{6283}{2000000000000}\times \frac{1946.56}{0.2\times 5\sqrt{12}}}$$

Multiply 0.2 and 5 to get 1.

$$\frac{500}{\frac{6283}{2000000000000}\times \frac{1946.56}{\sqrt{12}}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{500}{\frac{6283}{2000000000000}\times \frac{1946.56}{2\sqrt{3}}}$$

Rationalize the denominator of \frac{1946.56}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{500}{\frac{6283}{2000000000000}\times \frac{1946.56\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}}$$

The square of \sqrt{3} is 3.

$$\frac{500}{\frac{6283}{2000000000000}\times \frac{1946.56\sqrt{3}}{2\times 3}}$$

Multiply 2 and 3 to get 6.

$$\frac{500}{\frac{6283}{2000000000000}\times \frac{1946.56\sqrt{3}}{6}}$$

Divide 1946.56\sqrt{3} by 6 to get \frac{24332}{75}\sqrt{3}.

$$\frac{500}{\frac{6283}{2000000000000}\times \frac{24332}{75}\sqrt{3}}$$

Multiply \frac{6283}{2000000000000} and \frac{24332}{75} to get \frac{38219489}{37500000000000}.

$$\frac{500}{\frac{38219489}{37500000000000}\sqrt{3}}$$

Rationalize the denominator of \frac{500}{\frac{38219489}{37500000000000}\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{500\sqrt{3}}{\frac{38219489}{37500000000000}\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{500\sqrt{3}}{\frac{38219489}{37500000000000}\times 3}$$

Multiply \frac{38219489}{37500000000000} and 3 to get \frac{38219489}{12500000000000}.

$$\frac{500\sqrt{3}}{\frac{38219489}{12500000000000}}$$

Divide 500\sqrt{3} by \frac{38219489}{12500000000000} by multiplying 500\sqrt{3} by the reciprocal of \frac{38219489}{12500000000000}.

$$\frac{500\sqrt{3}\times 12500000000000}{38219489}$$

Multiply 500 and 12500000000000 to get 6250000000000000.

$$\frac{6250000000000000\sqrt{3}}{38219489}$$