Solve (sqrt{16}-6)^2*sqrt{-54/128}

$$( \sqrt { 16 } - 6 ) ^ { 2 } \times \sqrt { - \frac { 54 } { 128 } }$$

Evaluate (complex solution)

$$\frac{3\sqrt{3}i}{2}\approx 2.598076211i$$

Solution Steps

Calculate the square root of 16 and get 4.

$$\left(4-6\right)^{2}\sqrt{-\frac{54}{128}}$$

Subtract 6 from 4 to get -2.

$$\left(-2\right)^{2}\sqrt{-\frac{54}{128}}$$

Calculate -2 to the power of 2 and get 4.

$$4\sqrt{-\frac{54}{128}}$$

Reduce the fraction \frac{54}{128} to lowest terms by extracting and canceling out 2.

$$4\sqrt{-\frac{27}{64}}$$

Rewrite the square root of the division \sqrt{-\frac{27}{64}} as the division of square roots \frac{\sqrt{-27}}{\sqrt{64}}.

$$4\times \frac{\sqrt{-27}}{\sqrt{64}}$$

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}.

$$4\times \frac{3i\sqrt{3}}{\sqrt{64}}$$

Calculate the square root of 64 and get 8.

$$4\times \frac{3i\sqrt{3}}{8}$$

Divide 3i\sqrt{3} by 8 to get \frac{3}{8}i\sqrt{3}.

$$4\times \left(\frac{3}{8}i\right)\sqrt{3}$$

Multiply 4 and \frac{3}{8}i to get \frac{3}{2}i.

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

Real Part (complex solution)

$$0$$

Evaluate

$$\text{Indeterminate}$$