Because a radical has two solutions, the positive and negative. This means that √(a2b2) has twice as many solutions as ab. ab is in fact a subset of √(a2b2).
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I don't think you wanted the word "radical" in your question. Aren't you working with: C2 = A2 + B2 ? Or maybe: C = sqrt ( A2 + B2 ) ? In either case, A = sqrt ( C2 - B2 ). If your question is really the way you typed it, then the answer is more complicated.
The standard equation for an ellipse centered at the origin is [x2/a2] + [y2/b2] = 1 We also have the relationship, b2 = a2 - c2 where c is the distance of the foci from the centre and a & b are the half lengths of the major and minor axes respectively. When the length of the minor axis equals the distance between the two foci then 2b = 2c : b = c. Thus, a2 =b2 + c2 = 2b2 One of the formulae for the eccentricity of an ellipse is, e = √[(a2 - b2)/a2] Thus, e = √[(2b2 - b2) / 2b2] = √½ = 1/√2.
There are 3 main rules for expansion of algebraic expressions. They are as follows: 1) a2 _ b2 = (a-b) (a+b) 2) (a+b)2 = a2 + 2ab +b2 3) (a-b)2 = a2 - 2ab +b2
a3 + b3 = (a + b)(a2 - ab + b2) a3 - b3 = (a - b)(a2 + ab + b2)
(a3 + b3)/(a + b) = (a + b)*(a2 - ab + b2)/(a + b) = (a2 - ab + b2)