Solve sqrt{2*5.5/9.81}

$$\sqrt{ \frac{ 2 \cdot 5.5 }{ 9.81 } }$$

Evaluate

$$\frac{10\sqrt{1199}}{327}\approx 1.058916801$$

Solution Steps

Multiply 2 and 5.5 to get 11.

$$\sqrt{\frac{11}{9.81}}$$

Expand \frac{11}{9.81} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{1100}{981}}$$

Rewrite the square root of the division \sqrt{\frac{1100}{981}} as the division of square roots \frac{\sqrt{1100}}{\sqrt{981}}.

$$\frac{\sqrt{1100}}{\sqrt{981}}$$

Factor 1100=10^{2}\times 11. Rewrite the square root of the product \sqrt{10^{2}\times 11} as the product of square roots \sqrt{10^{2}}\sqrt{11}. Take the square root of 10^{2}.

$$\frac{10\sqrt{11}}{\sqrt{981}}$$

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}.

$$\frac{10\sqrt{11}}{3\sqrt{109}}$$

Rationalize the denominator of \frac{10\sqrt{11}}{3\sqrt{109}} by multiplying numerator and denominator by \sqrt{109}.

$$\frac{10\sqrt{11}\sqrt{109}}{3\left(\sqrt{109}\right)^{2}}$$

The square of \sqrt{109} is 109.

$$\frac{10\sqrt{11}\sqrt{109}}{3\times 109}$$

To multiply \sqrt{11} and \sqrt{109}, multiply the numbers under the square root.

$$\frac{10\sqrt{1199}}{3\times 109}$$

Multiply 3 and 109 to get 327.

$$\frac{10\sqrt{1199}}{327}$$