Solve 2*250/0.05^2*(1,26*10^-6*frac{8*1,58{sqrt{125}*0.2})^2}

$$\frac { 2 \cdot 250 } { 0.05 ^ { 2 } \cdot ( 1,26 \cdot 10 ^ { - 6 } \cdot \frac { 8 \cdot 1,58 } { \sqrt { 125 } \cdot 0.2 } ) ^ { 2 } }$$

Evaluate

$$\frac{97656250000000000000000}{24770529}\approx 3.942436998 \cdot 10^{15}$$

Solution Steps

Multiply 2 and 250 to get 500.

$$\frac{500}{0.05^{2}\times \left(1.26\times 10^{-6}\times \frac{8\times 1.58}{0.2\sqrt{125}}\right)^{2}}$$

Calculate 0.05 to the power of 2 and get 0.0025.

$$\frac{500}{0.0025\times \left(1.26\times 10^{-6}\times \frac{8\times 1.58}{0.2\sqrt{125}}\right)^{2}}$$

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

$$\frac{500}{0.0025\times \left(1.26\times \frac{1}{1000000}\times \frac{8\times 1.58}{0.2\sqrt{125}}\right)^{2}}$$

Multiply 1.26 and \frac{1}{1000000} to get \frac{63}{50000000}.

$$\frac{500}{0.0025\times \left(\frac{63}{50000000}\times \frac{8\times 1.58}{0.2\sqrt{125}}\right)^{2}}$$

Multiply 8 and 1.58 to get 12.64.

$$\frac{500}{0.0025\times \left(\frac{63}{50000000}\times \frac{12.64}{0.2\sqrt{125}}\right)^{2}}$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$\frac{500}{0.0025\times \left(\frac{63}{50000000}\times \frac{12.64}{0.2\times 5\sqrt{5}}\right)^{2}}$$

Multiply 0.2 and 5 to get 1.

$$\frac{500}{0.0025\times \left(\frac{63}{50000000}\times \frac{12.64}{\sqrt{5}}\right)^{2}}$$

Rationalize the denominator of \frac{12.64}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{500}{0.0025\times \left(\frac{63}{50000000}\times \frac{12.64\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{500}{0.0025\times \left(\frac{63}{50000000}\times \frac{12.64\sqrt{5}}{5}\right)^{2}}$$

Divide 12.64\sqrt{5} by 5 to get 2.528\sqrt{5}.

$$\frac{500}{0.0025\times \left(\frac{63}{50000000}\times 2.528\sqrt{5}\right)^{2}}$$

Multiply \frac{63}{50000000} and 2.528 to get \frac{4977}{1562500000}.

$$\frac{500}{0.0025\times \left(\frac{4977}{1562500000}\sqrt{5}\right)^{2}}$$

Expand \left(\frac{4977}{1562500000}\sqrt{5}\right)^{2}.

$$\frac{500}{0.0025\times \left(\frac{4977}{1562500000}\right)^{2}\left(\sqrt{5}\right)^{2}}$$

Calculate \frac{4977}{1562500000} to the power of 2 and get \frac{24770529}{2441406250000000000}.

$$\frac{500}{0.0025\times \frac{24770529}{2441406250000000000}\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{500}{0.0025\times \frac{24770529}{2441406250000000000}\times 5}$$

Multiply \frac{24770529}{2441406250000000000} and 5 to get \frac{24770529}{488281250000000000}.

$$\frac{500}{0.0025\times \frac{24770529}{488281250000000000}}$$

Multiply 0.0025 and \frac{24770529}{488281250000000000} to get \frac{24770529}{195312500000000000000}.

$$\frac{500}{\frac{24770529}{195312500000000000000}}$$

Divide 500 by \frac{24770529}{195312500000000000000} by multiplying 500 by the reciprocal of \frac{24770529}{195312500000000000000}.

$$500\times \frac{195312500000000000000}{24770529}$$

Multiply 500 and \frac{195312500000000000000}{24770529} to get \frac{97656250000000000000000}{24770529}.

$$\frac{97656250000000000000000}{24770529}$$

Factor

$$\frac{2 ^ {16} \cdot 5 ^ {26}}{3 ^ {4} \cdot 7 ^ {2} \cdot 79 ^ {2}} = 3942436998418564\frac{10952700}{24770529} = 3942436998418564.5$$