Solve =(372+0.5)-(1228/2)/sqrt{1228/2}

$$= \frac { ( 372 + 0.5 ) - ( 1228 / 2 ) } { \sqrt { 1228 } / 2 }$$

Evaluate

$$-\frac{483\sqrt{307}}{614}\approx -13.783133015$$

Solution Steps

Add 372 and 0.5 to get 372.5.

$$\frac{372.5-\frac{1228}{2}}{\frac{\sqrt{1228}}{2}}$$

Divide 1228 by 2 to get 614.

$$\frac{372.5-614}{\frac{\sqrt{1228}}{2}}$$

Subtract 614 from 372.5 to get -241.5.

$$\frac{-241.5}{\frac{\sqrt{1228}}{2}}$$

Factor 1228=2^{2}\times 307. Rewrite the square root of the product \sqrt{2^{2}\times 307} as the product of square roots \sqrt{2^{2}}\sqrt{307}. Take the square root of 2^{2}.

$$\frac{-241.5}{\frac{2\sqrt{307}}{2}}$$

Cancel out 2 and 2.

$$\frac{-241.5}{\sqrt{307}}$$

Rationalize the denominator of \frac{-241.5}{\sqrt{307}} by multiplying numerator and denominator by \sqrt{307}.

$$\frac{-241.5\sqrt{307}}{\left(\sqrt{307}\right)^{2}}$$

The square of \sqrt{307} is 307.

$$\frac{-241.5\sqrt{307}}{307}$$

Divide -241.5\sqrt{307} by 307 to get -\frac{483}{614}\sqrt{307}.

$$-\frac{483}{614}\sqrt{307}$$