Solve -1.182+2/sqrt{10}1.96

$$-1.182+ \frac{ 2 }{ \sqrt{ 10 } } 1.96$$

Evaluate

$$\frac{49\sqrt{10}}{125}-1.182\approx 0.057612843$$

Solution Steps

Rationalize the denominator of \frac{2}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$-1.182+1.96\times \frac{2\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$-1.182+1.96\times \frac{2\sqrt{10}}{10}$$

Divide 2\sqrt{10} by 10 to get \frac{1}{5}\sqrt{10}.

$$-1.182+1.96\times \frac{1}{5}\sqrt{10}$$

Convert decimal number 1.96 to fraction \frac{196}{100}. Reduce the fraction \frac{196}{100} to lowest terms by extracting and canceling out 4.

$$-1.182+\frac{49}{25}\times \frac{1}{5}\sqrt{10}$$

Multiply \frac{49}{25} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$-1.182+\frac{49\times 1}{25\times 5}\sqrt{10}$$

Do the multiplications in the fraction \frac{49\times 1}{25\times 5}.

$$-1.182+\frac{49}{125}\sqrt{10}$$