Solve 12/sqrt{1-frac{100{910^16}}}

$$\frac{ 12 }{ \sqrt{ 1- \frac{ 100 }{ 9 { 10 }^{ 16 } } } }$$

Evaluate

$$\frac{360000000\sqrt{899999999999999}}{899999999999999}\approx 12$$

Solution Steps

Calculate 10 to the power of 16 and get 10000000000000000.

$$\frac{12}{\sqrt{1-\frac{100}{9\times 10000000000000000}}}$$

Multiply 9 and 10000000000000000 to get 90000000000000000.

$$\frac{12}{\sqrt{1-\frac{100}{90000000000000000}}}$$

Reduce the fraction \frac{100}{90000000000000000} to lowest terms by extracting and canceling out 100.

$$\frac{12}{\sqrt{1-\frac{1}{900000000000000}}}$$

Convert 1 to fraction \frac{900000000000000}{900000000000000}.

$$\frac{12}{\sqrt{\frac{900000000000000}{900000000000000}-\frac{1}{900000000000000}}}$$

Since \frac{900000000000000}{900000000000000} and \frac{1}{900000000000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12}{\sqrt{\frac{900000000000000-1}{900000000000000}}}$$

Subtract 1 from 900000000000000 to get 899999999999999.

$$\frac{12}{\sqrt{\frac{899999999999999}{900000000000000}}}$$

Rewrite the square root of the division \sqrt{\frac{899999999999999}{900000000000000}} as the division of square roots \frac{\sqrt{899999999999999}}{\sqrt{900000000000000}}.

$$\frac{12}{\frac{\sqrt{899999999999999}}{\sqrt{900000000000000}}}$$

Calculate the square root of 900000000000000 and get 30000000.

$$\frac{12}{\frac{\sqrt{899999999999999}}{30000000}}$$

Divide 12 by \frac{\sqrt{899999999999999}}{30000000} by multiplying 12 by the reciprocal of \frac{\sqrt{899999999999999}}{30000000}.

$$\frac{12\times 30000000}{\sqrt{899999999999999}}$$

Rationalize the denominator of \frac{12\times 30000000}{\sqrt{899999999999999}} by multiplying numerator and denominator by \sqrt{899999999999999}.

$$\frac{12\times 30000000\sqrt{899999999999999}}{\left(\sqrt{899999999999999}\right)^{2}}$$

The square of \sqrt{899999999999999} is 899999999999999.

$$\frac{12\times 30000000\sqrt{899999999999999}}{899999999999999}$$

Multiply 12 and 30000000 to get 360000000.

$$\frac{360000000\sqrt{899999999999999}}{899999999999999}$$