Solve 12divfrac{sqrt{10}}{5}-1.6*50

$$12 \div \frac{ \sqrt{ 10 } }{ 5 } -1.6 \times 50$$

Evaluate

$$6\sqrt{10}-80\approx -61.026334039$$

Solution Steps

Divide 12 by \frac{\sqrt{10}}{5} by multiplying 12 by the reciprocal of \frac{\sqrt{10}}{5}.

$$\frac{12\times 5}{\sqrt{10}}-1.6\times 50$$

Multiply 12 and 5 to get 60.

$$\frac{60}{\sqrt{10}}-1.6\times 50$$

Rationalize the denominator of \frac{60}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{60\sqrt{10}}{\left(\sqrt{10}\right)^{2}}-1.6\times 50$$

The square of \sqrt{10} is 10.

$$\frac{60\sqrt{10}}{10}-1.6\times 50$$

Divide 60\sqrt{10} by 10 to get 6\sqrt{10}.

$$6\sqrt{10}-1.6\times 50$$

Multiply 1.6 and 50 to get 80.

$$6\sqrt{10}-80$$

Factor

$$6 \sqrt{10} - 80 = -61.026334039$$