Solve frac{sqrt{-18}}{sqrt{-27}}

$$\frac { \sqrt { - 18 } } { \sqrt { - 27 } }$$

Evaluate (complex solution)

$$\frac{\sqrt{6}}{3}\approx 0.816496581$$

Solution Steps

Factor -18=\left(3i\right)^{2}\times 2. Rewrite the square root of the product \sqrt{\left(3i\right)^{2}\times 2} as the product of square roots \sqrt{\left(3i\right)^{2}}\sqrt{2}. Take the square root of \left(3i\right)^{2}.

$$\frac{3i\sqrt{2}}{\sqrt{-27}}$$

Factor -27=\left(3i\right)^{2}\times 3. Rewrite the square root of the product \sqrt{\left(3i\right)^{2}\times 3} as the product of square roots \sqrt{\left(3i\right)^{2}}\sqrt{3}. Take the square root of \left(3i\right)^{2}.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{\sqrt{2}}{\sqrt{3}\times \left(3i\right)^{0}}$$

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{3}\times \left(3i\right)^{0}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}\times \left(3i\right)^{0}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{2}\sqrt{3}}{3\times \left(3i\right)^{0}}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{6}}{3\times \left(3i\right)^{0}}$$

Calculate 3i to the power of 0 and get 1.

$$\frac{\sqrt{6}}{3\times 1}$$

Multiply 3 and 1 to get 3.

$$\frac{\sqrt{6}}{3}$$

Real Part (complex solution)

$$\frac{\sqrt{6}}{3} = 0.8164965809277259$$

Evaluate

$$\text{Indeterminate}$$