Solve sqrt{131072/7813}

$$\sqrt{ \frac{ 131072 }{ 7813 } }$$

Evaluate

$$\frac{256\sqrt{15626}}{7813}\approx 4.095868934$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{131072}{7813}} as the division of square roots \frac{\sqrt{131072}}{\sqrt{7813}}.

$$\frac{\sqrt{131072}}{\sqrt{7813}}$$

Factor 131072=256^{2}\times 2. Rewrite the square root of the product \sqrt{256^{2}\times 2} as the product of square roots \sqrt{256^{2}}\sqrt{2}. Take the square root of 256^{2}.

$$\frac{256\sqrt{2}}{\sqrt{7813}}$$

Rationalize the denominator of \frac{256\sqrt{2}}{\sqrt{7813}} by multiplying numerator and denominator by \sqrt{7813}.

$$\frac{256\sqrt{2}\sqrt{7813}}{\left(\sqrt{7813}\right)^{2}}$$

The square of \sqrt{7813} is 7813.

$$\frac{256\sqrt{2}\sqrt{7813}}{7813}$$

To multiply \sqrt{2} and \sqrt{7813}, multiply the numbers under the square root.

$$\frac{256\sqrt{15626}}{7813}$$