Solve sqrt{45-57/14*65}

$$\sqrt{ 45- \frac{ 57 }{ 14 } \times 65 }$$

Evaluate (complex solution)

$$\frac{5\sqrt{1722}i}{14}\approx 14.820352801i$$

Solution Steps

Express \frac{57}{14}\times 65 as a single fraction.

$$\sqrt{45-\frac{57\times 65}{14}}$$

Multiply 57 and 65 to get 3705.

$$\sqrt{45-\frac{3705}{14}}$$

Convert 45 to fraction \frac{630}{14}.

$$\sqrt{\frac{630}{14}-\frac{3705}{14}}$$

Since \frac{630}{14} and \frac{3705}{14} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{630-3705}{14}}$$

Subtract 3705 from 630 to get -3075.

$$\sqrt{-\frac{3075}{14}}$$

Rewrite the square root of the division \sqrt{-\frac{3075}{14}} as the division of square roots \frac{\sqrt{-3075}}{\sqrt{14}}.

$$\frac{\sqrt{-3075}}{\sqrt{14}}$$

Factor -3075=\left(5i\right)^{2}\times 123. Rewrite the square root of the product \sqrt{\left(5i\right)^{2}\times 123} as the product of square roots \sqrt{\left(5i\right)^{2}}\sqrt{123}. Take the square root of \left(5i\right)^{2}.

$$\frac{5i\sqrt{123}}{\sqrt{14}}$$

Rationalize the denominator of \frac{5i\sqrt{123}}{\sqrt{14}} by multiplying numerator and denominator by \sqrt{14}.

$$\frac{5i\sqrt{123}\sqrt{14}}{\left(\sqrt{14}\right)^{2}}$$

The square of \sqrt{14} is 14.

$$\frac{5i\sqrt{123}\sqrt{14}}{14}$$

To multiply \sqrt{123} and \sqrt{14}, multiply the numbers under the square root.

$$\frac{5i\sqrt{1722}}{14}$$

Divide 5i\sqrt{1722} by 14 to get \frac{5}{14}i\sqrt{1722}.

$$\frac{5}{14}i\sqrt{1722}$$

Real Part (complex solution)

$$0$$

Evaluate

$$\text{Indeterminate}$$