Solve sqrt{2*2/9.81}

$$\sqrt{ \frac{ 2 \times 2 }{ 9.81 } }$$

Evaluate

$$\frac{20\sqrt{109}}{327}\approx 0.638550857$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\sqrt{\frac{4}{9.81}}$$

Expand \frac{4}{9.81} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{400}{981}}$$

Rewrite the square root of the division \sqrt{\frac{400}{981}} as the division of square roots \frac{\sqrt{400}}{\sqrt{981}}.

$$\frac{\sqrt{400}}{\sqrt{981}}$$

Calculate the square root of 400 and get 20.

$$\frac{20}{\sqrt{981}}$$

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}.

$$\frac{20}{3\sqrt{109}}$$

Rationalize the denominator of \frac{20}{3\sqrt{109}} by multiplying numerator and denominator by \sqrt{109}.

$$\frac{20\sqrt{109}}{3\left(\sqrt{109}\right)^{2}}$$

The square of \sqrt{109} is 109.

$$\frac{20\sqrt{109}}{3\times 109}$$

Multiply 3 and 109 to get 327.

$$\frac{20\sqrt{109}}{327}$$