Simplifying imaginary numbersi have the answer and steps, but i have no idea how to solve it. if anyone could . √-50=i√50=i•5√2 =5i√2so i'm guessing the 5 and 2 is factored from 50, but how are they picked?

First, you must factor a -1 from the number. -50 = -1 * 50. Then you separate the roots into the product of roots. The square root of -1 is i.

So far we took care of the negative root. Now you need to simplify the square root of 50. Since you are dealing with a square root, you need to find the largest perfect square integer that is a factor of 50. It happens to be 25. 25 is a perfect square integer since it is the square of 5, and 25 is the largest perfect square integer factor of 50 since 2 * 25 = 50. Now we factor 50 into 25 * 2, we separate the roots, and take out the root of 25.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584