Solve sqrt{9.8/9.81}

$$\sqrt{ \frac{ 9.8 }{ 9.81 } }$$

Evaluate

$$\frac{14\sqrt{545}}{327}\approx 0.999490186$$

Solution Steps

Expand \frac{9.8}{9.81} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{980}{981}}$$

Rewrite the square root of the division \sqrt{\frac{980}{981}} as the division of square roots \frac{\sqrt{980}}{\sqrt{981}}.

$$\frac{\sqrt{980}}{\sqrt{981}}$$

Factor 980=14^{2}\times 5. Rewrite the square root of the product \sqrt{14^{2}\times 5} as the product of square roots \sqrt{14^{2}}\sqrt{5}. Take the square root of 14^{2}.

$$\frac{14\sqrt{5}}{\sqrt{981}}$$

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}.

$$\frac{14\sqrt{5}}{3\sqrt{109}}$$

Rationalize the denominator of \frac{14\sqrt{5}}{3\sqrt{109}} by multiplying numerator and denominator by \sqrt{109}.

$$\frac{14\sqrt{5}\sqrt{109}}{3\left(\sqrt{109}\right)^{2}}$$

The square of \sqrt{109} is 109.

$$\frac{14\sqrt{5}\sqrt{109}}{3\times 109}$$

To multiply \sqrt{5} and \sqrt{109}, multiply the numbers under the square root.

$$\frac{14\sqrt{545}}{3\times 109}$$

Multiply 3 and 109 to get 327.

$$\frac{14\sqrt{545}}{327}$$