Solve =1190-1961/sqrt{frac{107{900}+142/400}}

$$= \frac { 1190 - 1961 } { \sqrt { \frac { 107 } { 900 } + \frac { 142 } { 400 } } }$$

Evaluate

$$-\frac{23130\sqrt{1706}}{853}\approx -1119.995080378$$

Solution Steps

Subtract 1961 from 1190 to get -771.

$$\frac{-771}{\sqrt{\frac{107}{900}+\frac{142}{400}}}$$

Reduce the fraction \frac{142}{400} to lowest terms by extracting and canceling out 2.

$$\frac{-771}{\sqrt{\frac{107}{900}+\frac{71}{200}}}$$

Least common multiple of 900 and 200 is 1800. Convert \frac{107}{900} and \frac{71}{200} to fractions with denominator 1800.

$$\frac{-771}{\sqrt{\frac{214}{1800}+\frac{639}{1800}}}$$

Since \frac{214}{1800} and \frac{639}{1800} have the same denominator, add them by adding their numerators.

$$\frac{-771}{\sqrt{\frac{214+639}{1800}}}$$

Add 214 and 639 to get 853.

$$\frac{-771}{\sqrt{\frac{853}{1800}}}$$

Rewrite the square root of the division \sqrt{\frac{853}{1800}} as the division of square roots \frac{\sqrt{853}}{\sqrt{1800}}.

$$\frac{-771}{\frac{\sqrt{853}}{\sqrt{1800}}}$$

Factor 1800=30^{2}\times 2. Rewrite the square root of the product \sqrt{30^{2}\times 2} as the product of square roots \sqrt{30^{2}}\sqrt{2}. Take the square root of 30^{2}.

$$\frac{-771}{\frac{\sqrt{853}}{30\sqrt{2}}}$$

Rationalize the denominator of \frac{\sqrt{853}}{30\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{-771}{\frac{\sqrt{853}\sqrt{2}}{30\left(\sqrt{2}\right)^{2}}}$$

The square of \sqrt{2} is 2.

$$\frac{-771}{\frac{\sqrt{853}\sqrt{2}}{30\times 2}}$$

To multiply \sqrt{853} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{-771}{\frac{\sqrt{1706}}{30\times 2}}$$

Multiply 30 and 2 to get 60.

$$\frac{-771}{\frac{\sqrt{1706}}{60}}$$

Divide -771 by \frac{\sqrt{1706}}{60} by multiplying -771 by the reciprocal of \frac{\sqrt{1706}}{60}.

$$\frac{-771\times 60}{\sqrt{1706}}$$

Rationalize the denominator of \frac{-771\times 60}{\sqrt{1706}} by multiplying numerator and denominator by \sqrt{1706}.

$$\frac{-771\times 60\sqrt{1706}}{\left(\sqrt{1706}\right)^{2}}$$

The square of \sqrt{1706} is 1706.

$$\frac{-771\times 60\sqrt{1706}}{1706}$$

Multiply -771 and 60 to get -46260.

$$\frac{-46260\sqrt{1706}}{1706}$$

Divide -46260\sqrt{1706} by 1706 to get -\frac{23130}{853}\sqrt{1706}.

$$-\frac{23130}{853}\sqrt{1706}$$