Solve 4*5/sqrt{2/5}

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

Evaluate

$$50\sqrt{2}\approx 70.710678119$$

Solution Steps

Multiply 4 and 5 to get 20.

$$\frac{20}{\frac{\sqrt{2}}{5}}$$

Divide 20 by \frac{\sqrt{2}}{5} by multiplying 20 by the reciprocal of \frac{\sqrt{2}}{5}.

$$\frac{20\times 5}{\sqrt{2}}$$

Rationalize the denominator of \frac{20\times 5}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{20\times 5\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{20\times 5\sqrt{2}}{2}$$

Multiply 20 and 5 to get 100.

$$\frac{100\sqrt{2}}{2}$$

Divide 100\sqrt{2} by 2 to get 50\sqrt{2}.

$$50\sqrt{2}$$