Solve {left(2sqrt{3-5}right)}^2

$${ \left(2 \sqrt{ 3-5 } \right) }^{ 2 }$$

Evaluate (complex solution)

$$-8$$

Solution Steps

Subtract 5 from 3 to get -2.

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

Factor -2=2\left(-1\right). Rewrite the square root of the product \sqrt{2\left(-1\right)} as the product of square roots \sqrt{2}\sqrt{-1}. By definition, the square root of -1 is i.

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

Multiply 2 and i to get 2i.

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

Expand \left(2i\sqrt{2}\right)^{2}.

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

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

$$-4\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$-4\times 2$$

Multiply -4 and 2 to get -8.

$$-8$$

Real Part (complex solution)

$$-8$$

Solution Steps

Subtract 5 from 3 to get -2.

$$Re(\left(2\sqrt{-2}\right)^{2})$$

Factor -2=2\left(-1\right). Rewrite the square root of the product \sqrt{2\left(-1\right)} as the product of square roots \sqrt{2}\sqrt{-1}. By definition, the square root of -1 is i.

$$Re(\left(2\sqrt{2}i\right)^{2})$$

Multiply 2 and i to get 2i.

$$Re(\left(2i\sqrt{2}\right)^{2})$$

Expand \left(2i\sqrt{2}\right)^{2}.

$$Re(\left(2i\right)^{2}\left(\sqrt{2}\right)^{2})$$

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

$$Re(-4\left(\sqrt{2}\right)^{2})$$

The square of \sqrt{2} is 2.

$$Re(-4\times 2)$$

Multiply -4 and 2 to get -8.

$$Re(-8)$$

The real part of -8 is -8.

$$-8$$

Evaluate

$$\text{Indeterminate}$$

Solution Steps

Subtract 5 from 3 to get -2.

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

Expand \left(2\sqrt{-2}\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

$$4\left(\sqrt{-2}\right)^{2}$$

Calculate \sqrt{-2} to the power of 2 and get -2.

$$4\left(-2\right)$$

Multiply 4 and -2 to get -8.

$$-8$$

Factor

$$\text{Indeterminate}$$