Solve sqrt{(25/14)^2-(5/2)^2}

$$\sqrt { ( \frac { 25 } { 14 } ) ^ { 2 } - ( \frac { 5 } { 2 } ) ^ { 2 } }$$

Evaluate (complex solution)

$$\frac{5\sqrt{6}i}{7}\approx 1.749635531i$$

Solution Steps

Calculate \frac{25}{14} to the power of 2 and get \frac{625}{196}.

$$\sqrt{\frac{625}{196}-\left(\frac{5}{2}\right)^{2}}$$

Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\sqrt{\frac{625}{196}-\frac{25}{4}}$$

Least common multiple of 196 and 4 is 196. Convert \frac{625}{196} and \frac{25}{4} to fractions with denominator 196.

$$\sqrt{\frac{625}{196}-\frac{1225}{196}}$$

Since \frac{625}{196} and \frac{1225}{196} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{625-1225}{196}}$$

Subtract 1225 from 625 to get -600.

$$\sqrt{\frac{-600}{196}}$$

Reduce the fraction \frac{-600}{196} to lowest terms by extracting and canceling out 4.

$$\sqrt{-\frac{150}{49}}$$

Rewrite the square root of the division \sqrt{-\frac{150}{49}} as the division of square roots \frac{\sqrt{-150}}{\sqrt{49}}.

$$\frac{\sqrt{-150}}{\sqrt{49}}$$

Factor -150=\left(5i\right)^{2}\times 6. Rewrite the square root of the product \sqrt{\left(5i\right)^{2}\times 6} as the product of square roots \sqrt{\left(5i\right)^{2}}\sqrt{6}. Take the square root of \left(5i\right)^{2}.

$$\frac{5i\sqrt{6}}{\sqrt{49}}$$

Calculate the square root of 49 and get 7.

$$\frac{5i\sqrt{6}}{7}$$

Divide 5i\sqrt{6} by 7 to get \frac{5}{7}i\sqrt{6}.

$$\frac{5}{7}i\sqrt{6}$$

Real Part (complex solution)

$$0$$

Evaluate

$$\text{Indeterminate}$$