Solve sqrt{(28/25)^2-(4/25i)^2}

$$\sqrt { ( \frac { 28 } { 25 } ) ^ { 2 } - ( \frac { 4 } { 25 } i ) ^ { 2 } }$$

Evaluate

$$\frac{4\sqrt{2}}{5}\approx 1.13137085$$

Solution Steps

Calculate \frac{28}{25} to the power of 2 and get \frac{784}{625}.

$$\sqrt{\frac{784}{625}-\left(\frac{4}{25}i\right)^{2}}$$

Calculate \frac{4}{25}i to the power of 2 and get -\frac{16}{625}.

$$\sqrt{\frac{784}{625}-\left(-\frac{16}{625}\right)}$$

The opposite of -\frac{16}{625} is \frac{16}{625}.

$$\sqrt{\frac{784}{625}+\frac{16}{625}}$$

Add \frac{784}{625} and \frac{16}{625} to get \frac{32}{25}.

$$\sqrt{\frac{32}{25}}$$

Rewrite the square root of the division \sqrt{\frac{32}{25}} as the division of square roots \frac{\sqrt{32}}{\sqrt{25}}.

$$\frac{\sqrt{32}}{\sqrt{25}}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$\frac{4\sqrt{2}}{\sqrt{25}}$$

Calculate the square root of 25 and get 5.

$$\frac{4\sqrt{2}}{5}$$

Real Part

$$\frac{4 \sqrt{2}}{5} = 1.131370849898476$$