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[ 2 - sqrt(-5) ]2 = [ 2 - i sqrt(5) ]2 = 4 + 5 -4i sqrt(5) = 9 - 4 i sqrt(5)
" i " = sqrt(-1)
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Well, isn't that a happy little math problem! The square root of 5 squared is 5, and the square root of 4 squared is 4. So, when you subtract 4 squared from 5 squared, you get 9. Remember, there are no mistakes in math, just happy little accidents!
5*root(21^2) = 5*21 = 105
b is the square root of 5/3
Call this number "x". In this case:x = root(5 root(5 root(5 root(5... Since the expression inside the first root is equal to the entire expression, you get: x = root(5 x) Squaring both sides, to get rid of the rood, you get: x squared = 5x x squared - 5x = 0 x(x - 5) = 0 So, x is either equal to 0, or to 5. Indeed, if you start with any number and repeatedly multiply by 5 and then take the square root, you get closer and closer to 5... unless you start with zero, in which case you get exactly zero.