Solve sqrt{38/981}

$$\sqrt{ \frac{ 38 }{ 981 } }$$

Evaluate

$$\frac{\sqrt{4142}}{327}\approx 0.196814592$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{38}{981}} as the division of square roots \frac{\sqrt{38}}{\sqrt{981}}.

$$\frac{\sqrt{38}}{\sqrt{981}}$$

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}.

$$\frac{\sqrt{38}}{3\sqrt{109}}$$

Rationalize the denominator of \frac{\sqrt{38}}{3\sqrt{109}} by multiplying numerator and denominator by \sqrt{109}.

$$\frac{\sqrt{38}\sqrt{109}}{3\left(\sqrt{109}\right)^{2}}$$

The square of \sqrt{109} is 109.

$$\frac{\sqrt{38}\sqrt{109}}{3\times 109}$$

To multiply \sqrt{38} and \sqrt{109}, multiply the numbers under the square root.

$$\frac{\sqrt{4142}}{3\times 109}$$

Multiply 3 and 109 to get 327.

$$\frac{\sqrt{4142}}{327}$$