Solve -3sqrt{-8/27}

$$- 3 \sqrt { - \frac { 8 } { 27 } }$$

Evaluate (complex solution)

$$-\frac{2\sqrt{6}i}{3}\approx -0-1.632993162i$$

Solution Steps

Rewrite the square root of the division \sqrt{-\frac{8}{27}} as the division of square roots \frac{\sqrt{-8}}{\sqrt{27}}.

$$-3\times \frac{\sqrt{-8}}{\sqrt{27}}$$

Factor -8=\left(2i\right)^{2}\times 2. Rewrite the square root of the product \sqrt{\left(2i\right)^{2}\times 2} as the product of square roots \sqrt{\left(2i\right)^{2}}\sqrt{2}. Take the square root of \left(2i\right)^{2}.

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

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

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

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

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

The square of \sqrt{3} is 3.

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

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

$$-3\times \frac{2i\sqrt{6}}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$-3\times \frac{2i\sqrt{6}}{9}$$

Divide 2i\sqrt{6} by 9 to get \frac{2}{9}i\sqrt{6}.

$$-3\times \left(\frac{2}{9}i\right)\sqrt{6}$$

Multiply -3 and \frac{2}{9}i to get -\frac{2}{3}i.

$$-\frac{2}{3}i\sqrt{6}$$

Real Part (complex solution)

$$0$$

Evaluate

$$\text{Indeterminate}$$