Solve sqrt{-4/-4-1}

$$\sqrt{ \frac{ -4 }{ -4-1 } }$$

Evaluate

$$\frac{2\sqrt{5}}{5}\approx 0.894427191$$

Solution Steps

Subtract 1 from -4 to get -5.

$$\sqrt{\frac{-4}{-5}}$$

Fraction \frac{-4}{-5} can be simplified to \frac{4}{5} by removing the negative sign from both the numerator and the denominator.

$$\sqrt{\frac{4}{5}}$$

Rewrite the square root of the division \sqrt{\frac{4}{5}} as the division of square roots \frac{\sqrt{4}}{\sqrt{5}}.

$$\frac{\sqrt{4}}{\sqrt{5}}$$

Calculate the square root of 4 and get 2.

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

Rationalize the denominator of \frac{2}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{2\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

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