Solve 1.87/5sqrt{2/4}

$$\frac{ 1.87 }{ \frac{ 5 \sqrt{ 2 } }{ 4 } }$$

Evaluate

$$\frac{187\sqrt{2}}{250}\approx 1.057831745$$

Solution Steps

Divide 1.87 by \frac{5\sqrt{2}}{4} by multiplying 1.87 by the reciprocal of \frac{5\sqrt{2}}{4}.

$$\frac{1.87\times 4}{5\sqrt{2}}$$

Multiply 1.87 and 4 to get 7.48.

$$\frac{7.48}{5\sqrt{2}}$$

Rationalize the denominator of \frac{7.48}{5\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{7.48\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{7.48\sqrt{2}}{5\times 2}$$

Multiply 5 and 2 to get 10.

$$\frac{7.48\sqrt{2}}{10}$$

Divide 7.48\sqrt{2} by 10 to get 0.748\sqrt{2}.

$$0.748\sqrt{2}$$