Solve 201.818-201.273/sqrt{43.101(frac{1{11}+1/11)}}=

$$\frac { 201.818 - 201.273 } { \sqrt { 43.101 ( \frac { 1 } { 11 } + \frac { 1 } { 11 } ) } } =$$

Evaluate

$$\frac{109\sqrt{263395}}{287340}\approx 0.194685754$$

Solution Steps

Subtract 201.273 from 201.818 to get 0.545.

$$\frac{0.545}{\sqrt{43.101\left(\frac{1}{11}+\frac{1}{11}\right)}}$$

Since \frac{1}{11} and \frac{1}{11} have the same denominator, add them by adding their numerators.

$$\frac{0.545}{\sqrt{43.101\times \frac{1+1}{11}}}$$

Add 1 and 1 to get 2.

$$\frac{0.545}{\sqrt{43.101\times \frac{2}{11}}}$$

Convert decimal number 43.101 to fraction \frac{43101}{1000}.

$$\frac{0.545}{\sqrt{\frac{43101}{1000}\times \frac{2}{11}}}$$

Multiply \frac{43101}{1000} times \frac{2}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{0.545}{\sqrt{\frac{43101\times 2}{1000\times 11}}}$$

Do the multiplications in the fraction \frac{43101\times 2}{1000\times 11}.

$$\frac{0.545}{\sqrt{\frac{86202}{11000}}}$$

Reduce the fraction \frac{86202}{11000} to lowest terms by extracting and canceling out 2.

$$\frac{0.545}{\sqrt{\frac{43101}{5500}}}$$

Rewrite the square root of the division \sqrt{\frac{43101}{5500}} as the division of square roots \frac{\sqrt{43101}}{\sqrt{5500}}.

$$\frac{0.545}{\frac{\sqrt{43101}}{\sqrt{5500}}}$$

Factor 43101=3^{2}\times 4789. Rewrite the square root of the product \sqrt{3^{2}\times 4789} as the product of square roots \sqrt{3^{2}}\sqrt{4789}. Take the square root of 3^{2}.

$$\frac{0.545}{\frac{3\sqrt{4789}}{\sqrt{5500}}}$$

Factor 5500=10^{2}\times 55. Rewrite the square root of the product \sqrt{10^{2}\times 55} as the product of square roots \sqrt{10^{2}}\sqrt{55}. Take the square root of 10^{2}.

$$\frac{0.545}{\frac{3\sqrt{4789}}{10\sqrt{55}}}$$

Rationalize the denominator of \frac{3\sqrt{4789}}{10\sqrt{55}} by multiplying numerator and denominator by \sqrt{55}.

$$\frac{0.545}{\frac{3\sqrt{4789}\sqrt{55}}{10\left(\sqrt{55}\right)^{2}}}$$

The square of \sqrt{55} is 55.

$$\frac{0.545}{\frac{3\sqrt{4789}\sqrt{55}}{10\times 55}}$$

To multiply \sqrt{4789} and \sqrt{55}, multiply the numbers under the square root.

$$\frac{0.545}{\frac{3\sqrt{263395}}{10\times 55}}$$

Multiply 10 and 55 to get 550.

$$\frac{0.545}{\frac{3\sqrt{263395}}{550}}$$

Divide 0.545 by \frac{3\sqrt{263395}}{550} by multiplying 0.545 by the reciprocal of \frac{3\sqrt{263395}}{550}.

$$\frac{0.545\times 550}{3\sqrt{263395}}$$

Rationalize the denominator of \frac{0.545\times 550}{3\sqrt{263395}} by multiplying numerator and denominator by \sqrt{263395}.

$$\frac{0.545\times 550\sqrt{263395}}{3\left(\sqrt{263395}\right)^{2}}$$

The square of \sqrt{263395} is 263395.

$$\frac{0.545\times 550\sqrt{263395}}{3\times 263395}$$

Multiply 0.545 and 550 to get 299.75.

$$\frac{299.75\sqrt{263395}}{3\times 263395}$$

Multiply 3 and 263395 to get 790185.

$$\frac{299.75\sqrt{263395}}{790185}$$

Divide 299.75\sqrt{263395} by 790185 to get \frac{109}{287340}\sqrt{263395}.

$$\frac{109}{287340}\sqrt{263395}$$