Solve sqrt{1+0,1/1-0,1}

$$\sqrt { \frac { 1 + 0,1 } { 1 - 0,1 } }$$

Evaluate

$$\frac{\sqrt{11}}{3}\approx 1.105541597$$

Solution Steps

Add 1 and 0,1 to get 1,1.

$$\sqrt{\frac{1,1}{1-0,1}}$$

Subtract 0,1 from 1 to get 0,9.

$$\sqrt{\frac{1,1}{0,9}}$$

Expand \frac{1,1}{0,9} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{11}{9}}$$

Rewrite the square root of the division \sqrt{\frac{11}{9}} as the division of square roots \frac{\sqrt{11}}{\sqrt{9}}.

$$\frac{\sqrt{11}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$\frac{\sqrt{11}}{3}$$