Solve -sqrt{1}+sqrt{-80}-sqrt{49}-sqrt{-5}

$$- \sqrt { 1 } + \sqrt { - 80 } - \sqrt { 49 } - \sqrt { - 5 }$$

Evaluate (complex solution)

$$-8+3\sqrt{5}i\approx -8+6.708203932i$$

Solution Steps

Calculate the square root of 1 and get 1.

$$-1+\sqrt{-80}-\sqrt{49}-\sqrt{-5}$$

Factor -80=\left(4i\right)^{2}\times 5. Rewrite the square root of the product \sqrt{\left(4i\right)^{2}\times 5} as the product of square roots \sqrt{\left(4i\right)^{2}}\sqrt{5}. Take the square root of \left(4i\right)^{2}.

$$-1+4i\sqrt{5}-\sqrt{49}-\sqrt{-5}$$

Calculate the square root of 49 and get 7.

$$-1+4i\sqrt{5}-7-\sqrt{-5}$$

Subtract 7 from -1 to get -8.

$$-8+4i\sqrt{5}-\sqrt{-5}$$

Factor -5=5\left(-1\right). Rewrite the square root of the product \sqrt{5\left(-1\right)} as the product of square roots \sqrt{5}\sqrt{-1}. By definition, the square root of -1 is i.

$$-8+4i\sqrt{5}-\sqrt{5}i$$

Multiply -1 and i to get -i.

$$-8+4i\sqrt{5}-i\sqrt{5}$$

Combine 4i\sqrt{5} and -i\sqrt{5} to get 3i\sqrt{5}.

$$-8+3i\sqrt{5}$$

Real Part (complex solution)

$$-8$$

Evaluate

$$\text{Indeterminate}$$