Solve sqrt{2*200/0.9*5*3.14}

$$\sqrt{ \frac{ 2 \times 200 }{ 0.9 \times 5 \times 3.14 } }$$

Evaluate

$$\frac{200\sqrt{157}}{471}\approx 5.32057923$$

Solution Steps

Cancel out 5 in both numerator and denominator.

$$\sqrt{\frac{2\times 40}{0.9\times 3.14}}$$

Multiply 2 and 40 to get 80.

$$\sqrt{\frac{80}{0.9\times 3.14}}$$

Multiply 0.9 and 3.14 to get 2.826.

$$\sqrt{\frac{80}{2.826}}$$

Expand \frac{80}{2.826} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{80000}{2826}}$$

Reduce the fraction \frac{80000}{2826} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{40000}{1413}}$$

Rewrite the square root of the division \sqrt{\frac{40000}{1413}} as the division of square roots \frac{\sqrt{40000}}{\sqrt{1413}}.

$$\frac{\sqrt{40000}}{\sqrt{1413}}$$

Calculate the square root of 40000 and get 200.

$$\frac{200}{\sqrt{1413}}$$

Factor 1413=3^{2}\times 157. Rewrite the square root of the product \sqrt{3^{2}\times 157} as the product of square roots \sqrt{3^{2}}\sqrt{157}. Take the square root of 3^{2}.

$$\frac{200}{3\sqrt{157}}$$

Rationalize the denominator of \frac{200}{3\sqrt{157}} by multiplying numerator and denominator by \sqrt{157}.

$$\frac{200\sqrt{157}}{3\left(\sqrt{157}\right)^{2}}$$

The square of \sqrt{157} is 157.

$$\frac{200\sqrt{157}}{3\times 157}$$

Multiply 3 and 157 to get 471.

$$\frac{200\sqrt{157}}{471}$$