Solve sqrt{2*200/1.4}

$$\sqrt{ \frac{ 2 \times 200 }{ 1.4 } }$$

Evaluate

$$\frac{20\sqrt{35}}{7}\approx 16.903085095$$

Solution Steps

Multiply 2 and 200 to get 400.

$$\sqrt{\frac{400}{1.4}}$$

Expand \frac{400}{1.4} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{4000}{14}}$$

Reduce the fraction \frac{4000}{14} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{2000}{7}}$$

Rewrite the square root of the division \sqrt{\frac{2000}{7}} as the division of square roots \frac{\sqrt{2000}}{\sqrt{7}}.

$$\frac{\sqrt{2000}}{\sqrt{7}}$$

Factor 2000=20^{2}\times 5. Rewrite the square root of the product \sqrt{20^{2}\times 5} as the product of square roots \sqrt{20^{2}}\sqrt{5}. Take the square root of 20^{2}.

$$\frac{20\sqrt{5}}{\sqrt{7}}$$

Rationalize the denominator of \frac{20\sqrt{5}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{20\sqrt{5}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{20\sqrt{5}\sqrt{7}}{7}$$

To multiply \sqrt{5} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{20\sqrt{35}}{7}$$