Solve sqrt{22528/992}

$$\sqrt{ \frac{ 22528 }{ 992 } }$$

Evaluate

$$\frac{8\sqrt{341}}{31}\approx 4.765467177$$

Solution Steps

Reduce the fraction \frac{22528}{992} to lowest terms by extracting and canceling out 32.

$$\sqrt{\frac{704}{31}}$$

Rewrite the square root of the division \sqrt{\frac{704}{31}} as the division of square roots \frac{\sqrt{704}}{\sqrt{31}}.

$$\frac{\sqrt{704}}{\sqrt{31}}$$

Factor 704=8^{2}\times 11. Rewrite the square root of the product \sqrt{8^{2}\times 11} as the product of square roots \sqrt{8^{2}}\sqrt{11}. Take the square root of 8^{2}.

$$\frac{8\sqrt{11}}{\sqrt{31}}$$

Rationalize the denominator of \frac{8\sqrt{11}}{\sqrt{31}} by multiplying numerator and denominator by \sqrt{31}.

$$\frac{8\sqrt{11}\sqrt{31}}{\left(\sqrt{31}\right)^{2}}$$

The square of \sqrt{31} is 31.

$$\frac{8\sqrt{11}\sqrt{31}}{31}$$

To multiply \sqrt{11} and \sqrt{31}, multiply the numbers under the square root.

$$\frac{8\sqrt{341}}{31}$$