Solve frac{sqrt{5}}{sqrt{-12}}=?

$$\frac { \sqrt { 5 } } { \sqrt { - 12 } } = ?$$

Evaluate (complex solution)

$$-\frac{\sqrt{15}i}{6}\approx -0-0.645497224i$$

Solution Steps

Factor -12=\left(2i\right)^{2}\times 3. Rewrite the square root of the product \sqrt{\left(2i\right)^{2}\times 3} as the product of square roots \sqrt{\left(2i\right)^{2}}\sqrt{3}. Take the square root of \left(2i\right)^{2}.

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

Rationalize the denominator of \frac{\sqrt{5}}{2i\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{5}\sqrt{3}}{2i\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

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

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{15}}{2i\times 3}$$

Multiply 2i and 3 to get 6i.

$$\frac{\sqrt{15}}{6i}$$

Real Part (complex solution)

$$0$$

Evaluate

$$\text{Indeterminate}$$