Solve sqrt{3856/81}

$$\sqrt { \frac { 3856 } { 81 } }$$

Evaluate

$$\frac{4\sqrt{241}}{9}\approx 6.899633198$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{3856}{81}} as the division of square roots \frac{\sqrt{3856}}{\sqrt{81}}.

$$\frac{\sqrt{3856}}{\sqrt{81}}$$

Factor 3856=4^{2}\times 241. Rewrite the square root of the product \sqrt{4^{2}\times 241} as the product of square roots \sqrt{4^{2}}\sqrt{241}. Take the square root of 4^{2}.

$$\frac{4\sqrt{241}}{\sqrt{81}}$$

Calculate the square root of 81 and get 9.

$$\frac{4\sqrt{241}}{9}$$