Solve 5/sqrt{1-frac{left(2.4*10^5*1000right)^2{9*3600^2*10^16}}}

$$\frac{ 5 }{ \sqrt{ 1- \frac{ { \left(2.4 \times { 10 }^{ 5 } \times 1000 \right) }^{ 2 } }{ 9 \times { 3600 }^{ 2 } \times { 10 }^{ 16 } } } }$$

Evaluate

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

Solution Steps

Calculate 10 to the power of 5 and get 100000.

$$\frac{5}{\sqrt{1-\frac{\left(2.4\times 100000\times 1000\right)^{2}}{9\times 3600^{2}\times 10^{16}}}}$$

Multiply 2.4 and 100000 to get 240000.

$$\frac{5}{\sqrt{1-\frac{\left(240000\times 1000\right)^{2}}{9\times 3600^{2}\times 10^{16}}}}$$

Multiply 240000 and 1000 to get 240000000.

$$\frac{5}{\sqrt{1-\frac{240000000^{2}}{9\times 3600^{2}\times 10^{16}}}}$$

Calculate 240000000 to the power of 2 and get 57600000000000000.

$$\frac{5}{\sqrt{1-\frac{57600000000000000}{9\times 3600^{2}\times 10^{16}}}}$$

Calculate 3600 to the power of 2 and get 12960000.

$$\frac{5}{\sqrt{1-\frac{57600000000000000}{9\times 12960000\times 10^{16}}}}$$

Multiply 9 and 12960000 to get 116640000.

$$\frac{5}{\sqrt{1-\frac{57600000000000000}{116640000\times 10^{16}}}}$$

Calculate 10 to the power of 16 and get 10000000000000000.

$$\frac{5}{\sqrt{1-\frac{57600000000000000}{116640000\times 10000000000000000}}}$$

Multiply 116640000 and 10000000000000000 to get 1166400000000000000000000.

$$\frac{5}{\sqrt{1-\frac{57600000000000000}{1166400000000000000000000}}}$$

Reduce the fraction \frac{57600000000000000}{1166400000000000000000000} to lowest terms by extracting and canceling out 57600000000000000.

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

Subtract \frac{1}{20250000} from 1 to get \frac{20249999}{20250000}.

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

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.

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