Solve sqrt{19,3-18,5/frac{1,33{30}+1,22/30}}=

$$\sqrt { \frac { 19,3 - 18,5 } { \frac { 1,33 } { 30 } + \frac { 1,22 } { 30 } } } =$$

Evaluate

$$\frac{4\sqrt{170}}{17}\approx 3.067859955$$

Solution Steps

Subtract 18,5 from 19,3 to get 0,8.

$$\sqrt{\frac{0,8}{\frac{1,33}{30}+\frac{1,22}{30}}}$$

Expand \frac{1,33}{30} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{0,8}{\frac{133}{3000}+\frac{1,22}{30}}}$$

Expand \frac{1,22}{30} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{0,8}{\frac{133}{3000}+\frac{122}{3000}}}$$

Since \frac{133}{3000} and \frac{122}{3000} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{0,8}{\frac{133+122}{3000}}}$$

Add 133 and 122 to get 255.

$$\sqrt{\frac{0,8}{\frac{255}{3000}}}$$

Reduce the fraction \frac{255}{3000} to lowest terms by extracting and canceling out 15.

$$\sqrt{\frac{0,8}{\frac{17}{200}}}$$

Divide 0,8 by \frac{17}{200} by multiplying 0,8 by the reciprocal of \frac{17}{200}.

$$\sqrt{0,8\times \frac{200}{17}}$$

Convert decimal number 0,8 to fraction \frac{8}{10}. Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{4}{5}\times \frac{200}{17}}$$

Multiply \frac{4}{5} times \frac{200}{17} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{4\times 200}{5\times 17}}$$

Do the multiplications in the fraction \frac{4\times 200}{5\times 17}.

$$\sqrt{\frac{800}{85}}$$

Reduce the fraction \frac{800}{85} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{160}{17}}$$

Rewrite the square root of the division \sqrt{\frac{160}{17}} as the division of square roots \frac{\sqrt{160}}{\sqrt{17}}.

$$\frac{\sqrt{160}}{\sqrt{17}}$$

Factor 160=4^{2}\times 10. Rewrite the square root of the product \sqrt{4^{2}\times 10} as the product of square roots \sqrt{4^{2}}\sqrt{10}. Take the square root of 4^{2}.

$$\frac{4\sqrt{10}}{\sqrt{17}}$$

Rationalize the denominator of \frac{4\sqrt{10}}{\sqrt{17}} by multiplying numerator and denominator by \sqrt{17}.

$$\frac{4\sqrt{10}\sqrt{17}}{\left(\sqrt{17}\right)^{2}}$$

The square of \sqrt{17} is 17.

$$\frac{4\sqrt{10}\sqrt{17}}{17}$$

To multiply \sqrt{10} and \sqrt{17}, multiply the numbers under the square root.

$$\frac{4\sqrt{170}}{17}$$