Solve =1190-1961/sqrt{frac{107{2}+142/1}}

$$= \frac { 1190 - 1961 } { \sqrt { \frac { 107 } { 2 } + \frac { 142 } { 1 } } }$$

Evaluate

$$-\frac{771\sqrt{782}}{391}\approx -55.141807423$$

Solution Steps

Subtract 1961 from 1190 to get -771.

$$\frac{-771}{\sqrt{\frac{107}{2}+\frac{142}{1}}}$$

Anything divided by one gives itself.

$$\frac{-771}{\sqrt{\frac{107}{2}+142}}$$

Convert 142 to fraction \frac{284}{2}.

$$\frac{-771}{\sqrt{\frac{107}{2}+\frac{284}{2}}}$$

Since \frac{107}{2} and \frac{284}{2} have the same denominator, add them by adding their numerators.

$$\frac{-771}{\sqrt{\frac{107+284}{2}}}$$

Add 107 and 284 to get 391.

$$\frac{-771}{\sqrt{\frac{391}{2}}}$$

Rewrite the square root of the division \sqrt{\frac{391}{2}} as the division of square roots \frac{\sqrt{391}}{\sqrt{2}}.

$$\frac{-771}{\frac{\sqrt{391}}{\sqrt{2}}}$$

Rationalize the denominator of \frac{\sqrt{391}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{-771}{\frac{\sqrt{391}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}$$

The square of \sqrt{2} is 2.

$$\frac{-771}{\frac{\sqrt{391}\sqrt{2}}{2}}$$

To multiply \sqrt{391} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{-771}{\frac{\sqrt{782}}{2}}$$

Divide -771 by \frac{\sqrt{782}}{2} by multiplying -771 by the reciprocal of \frac{\sqrt{782}}{2}.

$$\frac{-771\times 2}{\sqrt{782}}$$

Rationalize the denominator of \frac{-771\times 2}{\sqrt{782}} by multiplying numerator and denominator by \sqrt{782}.

$$\frac{-771\times 2\sqrt{782}}{\left(\sqrt{782}\right)^{2}}$$

The square of \sqrt{782} is 782.

$$\frac{-771\times 2\sqrt{782}}{782}$$

Multiply -771 and 2 to get -1542.

$$\frac{-1542\sqrt{782}}{782}$$

Divide -1542\sqrt{782} by 782 to get -\frac{771}{391}\sqrt{782}.

$$-\frac{771}{391}\sqrt{782}$$