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

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

Evaluate (complex solution)

$$\sqrt{3}i\approx 1.732050808i$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\sqrt{9-\left(2\sqrt{3}\right)^{2}}$$

Expand \left(2\sqrt{3}\right)^{2}.

$$\sqrt{9-2^{2}\left(\sqrt{3}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{3} is 3.

$$\sqrt{9-4\times 3}$$

Multiply 4 and 3 to get 12.

$$\sqrt{9-12}$$

Subtract 12 from 9 to get -3.

$$\sqrt{-3}$$

Factor -3=3\left(-1\right). Rewrite the square root of the product \sqrt{3\left(-1\right)} as the product of square roots \sqrt{3}\sqrt{-1}. By definition, the square root of -1 is i.

$$\sqrt{3}i$$

Evaluate

$$\text{Indeterminate}$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\sqrt{9-\left(2\sqrt{3}\right)^{2}}$$

Expand \left(2\sqrt{3}\right)^{2}.

$$\sqrt{9-2^{2}\left(\sqrt{3}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{3} is 3.

$$\sqrt{9-4\times 3}$$

Multiply 4 and 3 to get 12.

$$\sqrt{9-12}$$

Subtract 12 from 9 to get -3.

$$\sqrt{-3}$$

Real Part (complex solution)

$$0$$