Solve sqrt{1+01/1-0,1}

$$\sqrt { \frac { 1 + 01 } { 1 - 0,1 } }$$

Evaluate

$$\frac{2\sqrt{5}}{3}\approx 1.490711985$$

Solution Steps

Add 1 and 1 to get 2.

$$\sqrt{\frac{2}{1-0,1}}$$

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

$$\sqrt{\frac{2}{0,9}}$$

Expand \frac{2}{0,9} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{20}{9}}$$

Rewrite the square root of the division \sqrt{\frac{20}{9}} as the division of square roots \frac{\sqrt{20}}{\sqrt{9}}.

$$\frac{\sqrt{20}}{\sqrt{9}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{2\sqrt{5}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$\frac{2\sqrt{5}}{3}$$