Solve 0.192-0.068/sqrt{frac{1{25-3}+1/36-3}}

$$\frac{ 0.192-0.068 }{ \sqrt{ \frac{ 1 }{ 25-3 } + \frac{ 1 }{ 36-3 } } }$$

Evaluate

$$\frac{31\sqrt{330}}{1250}\approx 0.450514373$$

Solution Steps

Subtract 0.068 from 0.192 to get 0.124.

$$\frac{0.124}{\sqrt{\frac{1}{25-3}+\frac{1}{36-3}}}$$

Subtract 3 from 25 to get 22.

$$\frac{0.124}{\sqrt{\frac{1}{22}+\frac{1}{36-3}}}$$

Subtract 3 from 36 to get 33.

$$\frac{0.124}{\sqrt{\frac{1}{22}+\frac{1}{33}}}$$

Least common multiple of 22 and 33 is 66. Convert \frac{1}{22} and \frac{1}{33} to fractions with denominator 66.

$$\frac{0.124}{\sqrt{\frac{3}{66}+\frac{2}{66}}}$$

Since \frac{3}{66} and \frac{2}{66} have the same denominator, add them by adding their numerators.

$$\frac{0.124}{\sqrt{\frac{3+2}{66}}}$$

Add 3 and 2 to get 5.

$$\frac{0.124}{\sqrt{\frac{5}{66}}}$$

Rewrite the square root of the division \sqrt{\frac{5}{66}} as the division of square roots \frac{\sqrt{5}}{\sqrt{66}}.

$$\frac{0.124}{\frac{\sqrt{5}}{\sqrt{66}}}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{66}} by multiplying numerator and denominator by \sqrt{66}.

$$\frac{0.124}{\frac{\sqrt{5}\sqrt{66}}{\left(\sqrt{66}\right)^{2}}}$$

The square of \sqrt{66} is 66.

$$\frac{0.124}{\frac{\sqrt{5}\sqrt{66}}{66}}$$

To multiply \sqrt{5} and \sqrt{66}, multiply the numbers under the square root.

$$\frac{0.124}{\frac{\sqrt{330}}{66}}$$

Divide 0.124 by \frac{\sqrt{330}}{66} by multiplying 0.124 by the reciprocal of \frac{\sqrt{330}}{66}.

$$\frac{0.124\times 66}{\sqrt{330}}$$

Rationalize the denominator of \frac{0.124\times 66}{\sqrt{330}} by multiplying numerator and denominator by \sqrt{330}.

$$\frac{0.124\times 66\sqrt{330}}{\left(\sqrt{330}\right)^{2}}$$

The square of \sqrt{330} is 330.

$$\frac{0.124\times 66\sqrt{330}}{330}$$

Multiply 0.124 and 66 to get 8.184.

$$\frac{8.184\sqrt{330}}{330}$$

Divide 8.184\sqrt{330} by 330 to get 0.0248\sqrt{330}.

$$0.0248\sqrt{330}$$