Solve 5/sqrt{1-frac{5.76{9*3600^2}}}

$$\frac{ 5 }{ \sqrt{ 1- \frac{ 5.76 }{ 9 \times { 3600 }^{ 2 } } } }$$

Evaluate

$$\frac{22500\sqrt{20249999}}{20249999}\approx 5.000000123$$

Solution Steps

Calculate 3600 to the power of 2 and get 12960000.

$$\frac{5}{\sqrt{1-\frac{5.76}{9\times 12960000}}}$$

Multiply 9 and 12960000 to get 116640000.

$$\frac{5}{\sqrt{1-\frac{5.76}{116640000}}}$$

Expand \frac{5.76}{116640000} by multiplying both numerator and the denominator by 100.

$$\frac{5}{\sqrt{1-\frac{576}{11664000000}}}$$

Reduce the fraction \frac{576}{11664000000} to lowest terms by extracting and canceling out 576.

$$\frac{5}{\sqrt{1-\frac{1}{20250000}}}$$

Convert 1 to fraction \frac{20250000}{20250000}.

$$\frac{5}{\sqrt{\frac{20250000}{20250000}-\frac{1}{20250000}}}$$

Since \frac{20250000}{20250000} and \frac{1}{20250000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{\sqrt{\frac{20250000-1}{20250000}}}$$

Subtract 1 from 20250000 to get 20249999.

$$\frac{5}{\sqrt{\frac{20249999}{20250000}}}$$

Rewrite the square root of the division \sqrt{\frac{20249999}{20250000}} as the division of square roots \frac{\sqrt{20249999}}{\sqrt{20250000}}.

$$\frac{5}{\frac{\sqrt{20249999}}{\sqrt{20250000}}}$$

Calculate the square root of 20250000 and get 4500.

$$\frac{5}{\frac{\sqrt{20249999}}{4500}}$$

Divide 5 by \frac{\sqrt{20249999}}{4500} by multiplying 5 by the reciprocal of \frac{\sqrt{20249999}}{4500}.

$$\frac{5\times 4500}{\sqrt{20249999}}$$

Rationalize the denominator of \frac{5\times 4500}{\sqrt{20249999}} by multiplying numerator and denominator by \sqrt{20249999}.

$$\frac{5\times 4500\sqrt{20249999}}{\left(\sqrt{20249999}\right)^{2}}$$

The square of \sqrt{20249999} is 20249999.

$$\frac{5\times 4500\sqrt{20249999}}{20249999}$$

Multiply 5 and 4500 to get 22500.

$$\frac{22500\sqrt{20249999}}{20249999}$$