Solve -sqrt{9/4-3sqrt{(-3)^2}}+sqrt{(-2)^2*3^2}div(-sqrt{4})^2

$$- \sqrt { \frac { 9 } { 4 } - 3 \sqrt { ( - 3 ) ^ { 2 } } } + \sqrt { ( - 2 ) ^ { 2 } \times 3 ^ { 2 } } \div ( - \sqrt { 4 } ) ^ { 2 }$$

Evaluate (complex solution)

$$\frac{-3\sqrt{3}i+3}{2}\approx 1.5-2.598076211i$$

Solution Steps

Calculate -3 to the power of 2 and get 9.

$$-\sqrt{\frac{9}{4}-3\sqrt{9}}+\frac{\sqrt{\left(-2\right)^{2}\times 3^{2}}}{\left(-\sqrt{4}\right)^{2}}$$

Calculate the square root of 9 and get 3.

$$-\sqrt{\frac{9}{4}-3\times 3}+\frac{\sqrt{\left(-2\right)^{2}\times 3^{2}}}{\left(-\sqrt{4}\right)^{2}}$$

Multiply 3 and 3 to get 9.

$$-\sqrt{\frac{9}{4}-9}+\frac{\sqrt{\left(-2\right)^{2}\times 3^{2}}}{\left(-\sqrt{4}\right)^{2}}$$

Subtract 9 from \frac{9}{4} to get -\frac{27}{4}.

$$-\sqrt{-\frac{27}{4}}+\frac{\sqrt{\left(-2\right)^{2}\times 3^{2}}}{\left(-\sqrt{4}\right)^{2}}$$

Rewrite the square root of the division \sqrt{-\frac{27}{4}} as the division of square roots \frac{\sqrt{-27}}{\sqrt{4}}.

$$-\frac{\sqrt{-27}}{\sqrt{4}}+\frac{\sqrt{\left(-2\right)^{2}\times 3^{2}}}{\left(-\sqrt{4}\right)^{2}}$$

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}.

$$-\frac{3i\sqrt{3}}{\sqrt{4}}+\frac{\sqrt{\left(-2\right)^{2}\times 3^{2}}}{\left(-\sqrt{4}\right)^{2}}$$

Calculate the square root of 4 and get 2.

$$-\frac{3i\sqrt{3}}{2}+\frac{\sqrt{\left(-2\right)^{2}\times 3^{2}}}{\left(-\sqrt{4}\right)^{2}}$$

Divide 3i\sqrt{3} by 2 to get \frac{3}{2}i\sqrt{3}.

$$-\frac{3}{2}i\sqrt{3}+\frac{\sqrt{\left(-2\right)^{2}\times 3^{2}}}{\left(-\sqrt{4}\right)^{2}}$$

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

$$-\frac{3}{2}i\sqrt{3}+\frac{\sqrt{4\times 3^{2}}}{\left(-\sqrt{4}\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$-\frac{3}{2}i\sqrt{3}+\frac{\sqrt{4\times 9}}{\left(-\sqrt{4}\right)^{2}}$$

Multiply 4 and 9 to get 36.

$$-\frac{3}{2}i\sqrt{3}+\frac{\sqrt{36}}{\left(-\sqrt{4}\right)^{2}}$$

Calculate the square root of 36 and get 6.

$$-\frac{3}{2}i\sqrt{3}+\frac{6}{\left(-\sqrt{4}\right)^{2}}$$

Calculate the square root of 4 and get 2.

$$-\frac{3}{2}i\sqrt{3}+\frac{6}{\left(-2\right)^{2}}$$

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

$$-\frac{3}{2}i\sqrt{3}+\frac{6}{4}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

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

Real Part (complex solution)

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$

Evaluate

$$\text{Indeterminate}$$