Solve 1/sqrt{1-frac{2.7*10^8{3*10^8}}}

$$\frac{ 1 }{ \sqrt{ 1- \frac{ 2.7 \times { 10 }^{ 8 } }{ 3 \times { 10 }^{ 8 } } } }$$

Evaluate

$$\sqrt{10}\approx 3.16227766$$

Solution Steps

Cancel out 10^{8} in both numerator and denominator.

$$\frac{1}{\sqrt{1-\frac{2.7}{3}}}$$

Expand \frac{2.7}{3} by multiplying both numerator and the denominator by 10.

$$\frac{1}{\sqrt{1-\frac{27}{30}}}$$

Reduce the fraction \frac{27}{30} to lowest terms by extracting and canceling out 3.

$$\frac{1}{\sqrt{1-\frac{9}{10}}}$$

Convert 1 to fraction \frac{10}{10}.

$$\frac{1}{\sqrt{\frac{10}{10}-\frac{9}{10}}}$$

Since \frac{10}{10} and \frac{9}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{\sqrt{\frac{10-9}{10}}}$$

Subtract 9 from 10 to get 1.

$$\frac{1}{\sqrt{\frac{1}{10}}}$$

Rewrite the square root of the division \sqrt{\frac{1}{10}} as the division of square roots \frac{\sqrt{1}}{\sqrt{10}}.

$$\frac{1}{\frac{\sqrt{1}}{\sqrt{10}}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\frac{1}{\sqrt{10}}}$$

Rationalize the denominator of \frac{1}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{1}{\frac{\sqrt{10}}{\left(\sqrt{10}\right)^{2}}}$$

The square of \sqrt{10} is 10.

$$\frac{1}{\frac{\sqrt{10}}{10}}$$

Divide 1 by \frac{\sqrt{10}}{10} by multiplying 1 by the reciprocal of \frac{\sqrt{10}}{10}.

$$\frac{10}{\sqrt{10}}$$

Rationalize the denominator of \frac{10}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{10\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{10\sqrt{10}}{10}$$

Cancel out 10 and 10.

$$\sqrt{10}$$