Solve frac{sqrt{-30}}{sqrt{5}}

$$\frac { \sqrt { - 30 } } { \sqrt { 5 } }$$

Evaluate (complex solution)

$$\sqrt{6}i\approx 2.449489743i$$

Solution Steps

Factor -30=30\left(-1\right). Rewrite the square root of the product \sqrt{30\left(-1\right)} as the product of square roots \sqrt{30}\sqrt{-1}. By definition, the square root of -1 is i.

$$\frac{\sqrt{30}i}{\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{30}i}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{30}i\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{30}i\sqrt{5}}{5}$$

Factor 30=5\times 6. Rewrite the square root of the product \sqrt{5\times 6} as the product of square roots \sqrt{5}\sqrt{6}.

$$\frac{\sqrt{5}\sqrt{6}i\sqrt{5}}{5}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{5i\sqrt{6}}{5}$$

Divide 5i\sqrt{6} by 5 to get i\sqrt{6}.

$$i\sqrt{6}$$

Real Part (complex solution)

$$0$$

Evaluate

$$\text{Indeterminate}$$