Solve 187/5sqrt{2/4}=

$$\frac{ 187 }{ \frac{ 5 \sqrt{ 2 } }{ 4 } } =$$

Evaluate

$$\frac{374\sqrt{2}}{5}\approx 105.783174466$$

Solution Steps

Divide 187 by \frac{5\sqrt{2}}{4} by multiplying 187 by the reciprocal of \frac{5\sqrt{2}}{4}.

$$\frac{187\times 4}{5\sqrt{2}}$$

Multiply 187 and 4 to get 748.

$$\frac{748}{5\sqrt{2}}$$

Rationalize the denominator of \frac{748}{5\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{748\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{748\sqrt{2}}{5\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{374\sqrt{2}}{5}$$