Solve sqrt{113.6/1.1}

$$\sqrt { \frac { 113.6 } { 1.1 } }$$

Evaluate

$$\frac{4\sqrt{781}}{11}\approx 10.162318991$$

Solution Steps

Expand \frac{113.6}{1.1} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{1136}{11}}$$

Rewrite the square root of the division \sqrt{\frac{1136}{11}} as the division of square roots \frac{\sqrt{1136}}{\sqrt{11}}.

$$\frac{\sqrt{1136}}{\sqrt{11}}$$

Factor 1136=4^{2}\times 71. Rewrite the square root of the product \sqrt{4^{2}\times 71} as the product of square roots \sqrt{4^{2}}\sqrt{71}. Take the square root of 4^{2}.

$$\frac{4\sqrt{71}}{\sqrt{11}}$$

Rationalize the denominator of \frac{4\sqrt{71}}{\sqrt{11}} by multiplying numerator and denominator by \sqrt{11}.

$$\frac{4\sqrt{71}\sqrt{11}}{\left(\sqrt{11}\right)^{2}}$$

The square of \sqrt{11} is 11.

$$\frac{4\sqrt{71}\sqrt{11}}{11}$$

To multiply \sqrt{71} and \sqrt{11}, multiply the numbers under the square root.

$$\frac{4\sqrt{781}}{11}$$