Solve sqrt{-3}*sqrt{27}

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

Evaluate (complex solution)

$$9i$$

Solution Steps

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.

$$\sqrt{3}i\sqrt{27}$$

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}.

$$\sqrt{3}i\times 3\sqrt{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$3\times \left(3i\right)$$

Multiply 3 and 3i to get 9i.

$$9i$$

Real Part (complex solution)

$$0$$

Solution Steps

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.

$$Re(\sqrt{3}i\sqrt{27})$$

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}.

$$Re(\sqrt{3}i\times 3\sqrt{3})$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$Re(3\times \left(3i\right))$$

Multiply 3 and 3i to get 9i.

$$Re(9i)$$

The real part of 9i is 0.

$$0$$

Evaluate

$$\text{Indeterminate}$$