Solve -1.182-2/sqrt{10}*(1.96)

$$- 1.182 - \frac { 2 } { \sqrt { 10 } } \cdot ( 1.96 )$$

Evaluate

$$-\frac{49\sqrt{10}}{125}-1.182\approx -2.421612843$$

Solution Steps

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

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

The square of \sqrt{10} is 10.

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

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

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

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.

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

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

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

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

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