Solve sqrt{2(1.9)/9.81}

$$\sqrt{ \frac{ 2(1.9) }{ 9.81 } }$$

Evaluate

$$\frac{2\sqrt{10355}}{327}\approx 0.622382388$$

Solution Steps

Multiply 2 and 1.9 to get 3.8.

$$\sqrt{\frac{3.8}{9.81}}$$

Expand \frac{3.8}{9.81} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{380}{981}}$$

Rewrite the square root of the division \sqrt{\frac{380}{981}} as the division of square roots \frac{\sqrt{380}}{\sqrt{981}}.

$$\frac{\sqrt{380}}{\sqrt{981}}$$

Factor 380=2^{2}\times 95. Rewrite the square root of the product \sqrt{2^{2}\times 95} as the product of square roots \sqrt{2^{2}}\sqrt{95}. Take the square root of 2^{2}.

$$\frac{2\sqrt{95}}{\sqrt{981}}$$

Factor 981=3^{2}\times 109. Rewrite the square root of the product \sqrt{3^{2}\times 109} as the product of square roots \sqrt{3^{2}}\sqrt{109}. Take the square root of 3^{2}.

$$\frac{2\sqrt{95}}{3\sqrt{109}}$$

Rationalize the denominator of \frac{2\sqrt{95}}{3\sqrt{109}} by multiplying numerator and denominator by \sqrt{109}.

$$\frac{2\sqrt{95}\sqrt{109}}{3\left(\sqrt{109}\right)^{2}}$$

The square of \sqrt{109} is 109.

$$\frac{2\sqrt{95}\sqrt{109}}{3\times 109}$$

To multiply \sqrt{95} and \sqrt{109}, multiply the numbers under the square root.

$$\frac{2\sqrt{10355}}{3\times 109}$$

Multiply 3 and 109 to get 327.

$$\frac{2\sqrt{10355}}{327}$$