Solve 160-200*0.7/sqrt{0.7*0.3*200}

$$\frac{ 160-200 \times 0.7 }{ \sqrt{ 0.7 \times 0.3 \times 200 } }$$

Evaluate

$$\frac{10\sqrt{42}}{21}\approx 3.086066999$$

Solution Steps

Multiply 200 and 0.7 to get 140.

$$\frac{160-140}{\sqrt{0.7\times 0.3\times 200}}$$

Subtract 140 from 160 to get 20.

$$\frac{20}{\sqrt{0.7\times 0.3\times 200}}$$

Multiply 0.7 and 0.3 to get 0.21.

$$\frac{20}{\sqrt{0.21\times 200}}$$

Multiply 0.21 and 200 to get 42.

$$\frac{20}{\sqrt{42}}$$

Rationalize the denominator of \frac{20}{\sqrt{42}} by multiplying numerator and denominator by \sqrt{42}.

$$\frac{20\sqrt{42}}{\left(\sqrt{42}\right)^{2}}$$

The square of \sqrt{42} is 42.

$$\frac{20\sqrt{42}}{42}$$

Divide 20\sqrt{42} by 42 to get \frac{10}{21}\sqrt{42}.

$$\frac{10}{21}\sqrt{42}$$