Solve sqrt{98/981}

$$\sqrt{ \frac{ 98 }{ 981 } }$$

Evaluate

$$\frac{7\sqrt{218}}{327}\approx 0.316066549$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{98}{981}} as the division of square roots \frac{\sqrt{98}}{\sqrt{981}}.

$$\frac{\sqrt{98}}{\sqrt{981}}$$

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$\frac{7\sqrt{2}}{\sqrt{981}}$$

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}.

$$\frac{7\sqrt{2}}{3\sqrt{109}}$$

Rationalize the denominator of \frac{7\sqrt{2}}{3\sqrt{109}} by multiplying numerator and denominator by \sqrt{109}.

$$\frac{7\sqrt{2}\sqrt{109}}{3\left(\sqrt{109}\right)^{2}}$$

The square of \sqrt{109} is 109.

$$\frac{7\sqrt{2}\sqrt{109}}{3\times 109}$$

To multiply \sqrt{2} and \sqrt{109}, multiply the numbers under the square root.

$$\frac{7\sqrt{218}}{3\times 109}$$

Multiply 3 and 109 to get 327.

$$\frac{7\sqrt{218}}{327}$$