Solve 687-19546^2/sqrt{57662}

$$687 - 195 \frac { 46 ^ { 2 } } { \sqrt { 57662 } }$$

Evaluate

$$-\frac{206310\sqrt{57662}}{28831}+687\approx -1031.325455512$$

Solution Steps

Calculate 46 to the power of 2 and get 2116.

$$687-195\times \frac{2116}{\sqrt{57662}}$$

Rationalize the denominator of \frac{2116}{\sqrt{57662}} by multiplying numerator and denominator by \sqrt{57662}.

$$687-195\times \frac{2116\sqrt{57662}}{\left(\sqrt{57662}\right)^{2}}$$

The square of \sqrt{57662} is 57662.

$$687-195\times \frac{2116\sqrt{57662}}{57662}$$

Divide 2116\sqrt{57662} by 57662 to get \frac{1058}{28831}\sqrt{57662}.

$$687-195\times \frac{1058}{28831}\sqrt{57662}$$

Express 195\times \frac{1058}{28831} as a single fraction.

$$687-\frac{195\times 1058}{28831}\sqrt{57662}$$

Multiply 195 and 1058 to get 206310.

$$687-\frac{206310}{28831}\sqrt{57662}$$

Factor

$$\frac{3 {(6602299 - 68770 \sqrt{57662})}}{28831} = -1031.3254555115366$$