Solve sqrt{25/frac{3{4}-6}}59

$$\sqrt{ \frac{ 25 }{ \frac{ 3 }{ 4 } -6 } } 59$$

Evaluate (complex solution)

$$\frac{590\sqrt{21}i}{21}\approx 128.748555239i$$

Solution Steps

Convert 6 to fraction \frac{24}{4}.

$$59\sqrt{\frac{25}{\frac{3}{4}-\frac{24}{4}}}$$

Since \frac{3}{4} and \frac{24}{4} have the same denominator, subtract them by subtracting their numerators.

$$59\sqrt{\frac{25}{\frac{3-24}{4}}}$$

Subtract 24 from 3 to get -21.

$$59\sqrt{\frac{25}{-\frac{21}{4}}}$$

Divide 25 by -\frac{21}{4} by multiplying 25 by the reciprocal of -\frac{21}{4}.

$$59\sqrt{25\left(-\frac{4}{21}\right)}$$

Express 25\left(-\frac{4}{21}\right) as a single fraction.

$$59\sqrt{\frac{25\left(-4\right)}{21}}$$

Multiply 25 and -4 to get -100.

$$59\sqrt{\frac{-100}{21}}$$

Fraction \frac{-100}{21} can be rewritten as -\frac{100}{21} by extracting the negative sign.

$$59\sqrt{-\frac{100}{21}}$$

Rewrite the square root of the division \sqrt{-\frac{100}{21}} as the division of square roots \frac{\sqrt{-100}}{\sqrt{21}}.

$$59\times \frac{\sqrt{-100}}{\sqrt{21}}$$

Calculate the square root of -100 and get 10i.

$$59\times \frac{10i}{\sqrt{21}}$$

Rationalize the denominator of \frac{10i}{\sqrt{21}} by multiplying numerator and denominator by \sqrt{21}.

$$59\times \frac{10i\sqrt{21}}{\left(\sqrt{21}\right)^{2}}$$

The square of \sqrt{21} is 21.

$$59\times \frac{10i\sqrt{21}}{21}$$

Divide 10i\sqrt{21} by 21 to get \frac{10}{21}i\sqrt{21}.

$$59\times \left(\frac{10}{21}i\right)\sqrt{21}$$

Multiply 59 and \frac{10}{21}i to get \frac{590}{21}i.

$$\frac{590}{21}i\sqrt{21}$$

Real Part (complex solution)

$$0$$

Evaluate

$$\text{Indeterminate}$$