Solve sqrt{78div79-7}

$$\sqrt{ 78 \div 79-7 }$$

Evaluate (complex solution)

$$\frac{5\sqrt{1501}i}{79}\approx 2.452072231i$$

Solution Steps

Convert 7 to fraction \frac{553}{79}.

$$\sqrt{\frac{78}{79}-\frac{553}{79}}$$

Since \frac{78}{79} and \frac{553}{79} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{78-553}{79}}$$

Subtract 553 from 78 to get -475.

$$\sqrt{-\frac{475}{79}}$$

Rewrite the square root of the division \sqrt{-\frac{475}{79}} as the division of square roots \frac{\sqrt{-475}}{\sqrt{79}}.

$$\frac{\sqrt{-475}}{\sqrt{79}}$$

Factor -475=\left(5i\right)^{2}\times 19. Rewrite the square root of the product \sqrt{\left(5i\right)^{2}\times 19} as the product of square roots \sqrt{\left(5i\right)^{2}}\sqrt{19}. Take the square root of \left(5i\right)^{2}.

$$\frac{5i\sqrt{19}}{\sqrt{79}}$$

Rationalize the denominator of \frac{5i\sqrt{19}}{\sqrt{79}} by multiplying numerator and denominator by \sqrt{79}.

$$\frac{5i\sqrt{19}\sqrt{79}}{\left(\sqrt{79}\right)^{2}}$$

The square of \sqrt{79} is 79.

$$\frac{5i\sqrt{19}\sqrt{79}}{79}$$

To multiply \sqrt{19} and \sqrt{79}, multiply the numbers under the square root.

$$\frac{5i\sqrt{1501}}{79}$$

Divide 5i\sqrt{1501} by 79 to get \frac{5}{79}i\sqrt{1501}.

$$\frac{5}{79}i\sqrt{1501}$$

Real Part (complex solution)

$$0$$

Evaluate

$$\text{Indeterminate}$$