Solve frac{sqrt{-50}}{5isqrt{-2}}

$$\frac { \sqrt { - 50 } } { 5 i \sqrt { - 2 } }$$

Evaluate

$$-i$$

Solution Steps

Factor -50=\left(5i\right)^{2}\times 2. Rewrite the square root of the product \sqrt{\left(5i\right)^{2}\times 2} as the product of square roots \sqrt{\left(5i\right)^{2}}\sqrt{2}. Take the square root of \left(5i\right)^{2}.

$$\frac{5i\sqrt{2}}{5i\sqrt{-2}}$$

Factor -2=2\left(-1\right). Rewrite the square root of the product \sqrt{2\left(-1\right)} as the product of square roots \sqrt{2}\sqrt{-1}. By definition, the square root of -1 is i.

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

Multiply 5i and i to get -5.

$$\frac{5i\sqrt{2}}{-5\sqrt{2}}$$

Cancel out \sqrt{2} in both numerator and denominator.

$$\frac{5i}{-5}$$

Divide 5i by -5 to get -i.

$$-i$$

Real Part

$$0$$

Solution Steps

Factor -50=\left(5i\right)^{2}\times 2. Rewrite the square root of the product \sqrt{\left(5i\right)^{2}\times 2} as the product of square roots \sqrt{\left(5i\right)^{2}}\sqrt{2}. Take the square root of \left(5i\right)^{2}.

$$Re(\frac{5i\sqrt{2}}{5i\sqrt{-2}})$$

Factor -2=2\left(-1\right). Rewrite the square root of the product \sqrt{2\left(-1\right)} as the product of square roots \sqrt{2}\sqrt{-1}. By definition, the square root of -1 is i.

$$Re(\frac{5i\sqrt{2}}{5i\sqrt{2}i})$$

Multiply 5i and i to get -5.

$$Re(\frac{5i\sqrt{2}}{-5\sqrt{2}})$$

Cancel out \sqrt{2} in both numerator and denominator.

$$Re(\frac{5i}{-5})$$

Divide 5i by -5 to get -i.

$$Re(-i)$$

The real part of -i is 0.

$$0$$