Solve 687-1.964.6^2/sqrt{57662}

$$687-1.96 \frac{ { 4.6 }^{ 2 } }{ \sqrt{ 57662 } }$$

Evaluate

$$-\frac{25921\sqrt{57662}}{36038750}+687\approx 686.827286262$$

Solution Steps

Calculate 4.6 to the power of 2 and get 21.16.

$$687-1.96\times \frac{21.16}{\sqrt{57662}}$$

Rationalize the denominator of \frac{21.16}{\sqrt{57662}} by multiplying numerator and denominator by \sqrt{57662}.

$$687-1.96\times \frac{21.16\sqrt{57662}}{\left(\sqrt{57662}\right)^{2}}$$

The square of \sqrt{57662} is 57662.

$$687-1.96\times \frac{21.16\sqrt{57662}}{57662}$$

Divide 21.16\sqrt{57662} by 57662 to get \frac{529}{1441550}\sqrt{57662}.

$$687-1.96\times \frac{529}{1441550}\sqrt{57662}$$

Multiply 1.96 and \frac{529}{1441550} to get \frac{25921}{36038750}.

$$687-\frac{25921}{36038750}\sqrt{57662}$$