Solve 175.833-175.222/sqrt{33.275left(frac{1{18}+1/18right)}}

$$\frac{ 175.833-175.222 }{ \sqrt{ 33.275 \left( \frac{ 1 }{ 18 } + \frac{ 1 }{ 18 } \right) } }$$

Evaluate

$$\frac{1833\sqrt{110}}{60500}\approx 0.317763077$$

Solution Steps

Subtract 175.222 from 175.833 to get 0.611.

$$\frac{0.611}{\sqrt{33.275\left(\frac{1}{18}+\frac{1}{18}\right)}}$$

Since \frac{1}{18} and \frac{1}{18} have the same denominator, add them by adding their numerators.

$$\frac{0.611}{\sqrt{33.275\times \frac{1+1}{18}}}$$

Add 1 and 1 to get 2.

$$\frac{0.611}{\sqrt{33.275\times \frac{2}{18}}}$$

Reduce the fraction \frac{2}{18} to lowest terms by extracting and canceling out 2.

$$\frac{0.611}{\sqrt{33.275\times \frac{1}{9}}}$$

Convert decimal number 33.275 to fraction \frac{33275}{1000}. Reduce the fraction \frac{33275}{1000} to lowest terms by extracting and canceling out 25.

$$\frac{0.611}{\sqrt{\frac{1331}{40}\times \frac{1}{9}}}$$

Multiply \frac{1331}{40} times \frac{1}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{0.611}{\sqrt{\frac{1331\times 1}{40\times 9}}}$$

Do the multiplications in the fraction \frac{1331\times 1}{40\times 9}.

$$\frac{0.611}{\sqrt{\frac{1331}{360}}}$$

Rewrite the square root of the division \sqrt{\frac{1331}{360}} as the division of square roots \frac{\sqrt{1331}}{\sqrt{360}}.

$$\frac{0.611}{\frac{\sqrt{1331}}{\sqrt{360}}}$$

Factor 1331=11^{2}\times 11. Rewrite the square root of the product \sqrt{11^{2}\times 11} as the product of square roots \sqrt{11^{2}}\sqrt{11}. Take the square root of 11^{2}.

$$\frac{0.611}{\frac{11\sqrt{11}}{\sqrt{360}}}$$

Factor 360=6^{2}\times 10. Rewrite the square root of the product \sqrt{6^{2}\times 10} as the product of square roots \sqrt{6^{2}}\sqrt{10}. Take the square root of 6^{2}.

$$\frac{0.611}{\frac{11\sqrt{11}}{6\sqrt{10}}}$$

Rationalize the denominator of \frac{11\sqrt{11}}{6\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{0.611}{\frac{11\sqrt{11}\sqrt{10}}{6\left(\sqrt{10}\right)^{2}}}$$

The square of \sqrt{10} is 10.

$$\frac{0.611}{\frac{11\sqrt{11}\sqrt{10}}{6\times 10}}$$

To multiply \sqrt{11} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{0.611}{\frac{11\sqrt{110}}{6\times 10}}$$

Multiply 6 and 10 to get 60.

$$\frac{0.611}{\frac{11\sqrt{110}}{60}}$$

Divide 0.611 by \frac{11\sqrt{110}}{60} by multiplying 0.611 by the reciprocal of \frac{11\sqrt{110}}{60}.

$$\frac{0.611\times 60}{11\sqrt{110}}$$

Rationalize the denominator of \frac{0.611\times 60}{11\sqrt{110}} by multiplying numerator and denominator by \sqrt{110}.

$$\frac{0.611\times 60\sqrt{110}}{11\left(\sqrt{110}\right)^{2}}$$

The square of \sqrt{110} is 110.

$$\frac{0.611\times 60\sqrt{110}}{11\times 110}$$

Multiply 0.611 and 60 to get 36.66.

$$\frac{36.66\sqrt{110}}{11\times 110}$$

Multiply 11 and 110 to get 1210.

$$\frac{36.66\sqrt{110}}{1210}$$

Divide 36.66\sqrt{110} by 1210 to get \frac{1833}{60500}\sqrt{110}.

$$\frac{1833}{60500}\sqrt{110}$$