Is (square root of x) to the second power = x an identity (true for all non negative values of x and why?

(square root of x) to the second power is equal to the square root of (x square). This is pactially the same concept of order of opertations just like you can divide and multliply in different order and still get the same result.Is (square root of x) to the second power = x an identity (true for all non negative values of x and why?
When you take a square root of a negative value you get an imaginary number because sqr (-1) is equal to the imaginary number i


so then sqr (-16) = 4i


but if you then square this imaginary figure, you will get back to the original figure so sqr (x) times sqr (x) is always equal to x even if x is negative





these imaginary figures can have a real part too for example 4+2i where 4 would be the real part and 2i the imaginary part so you could do these type of calculations :


4+2i squared = 12+16i


and in general :


a+bi times c+di = ac-bd + adi+bci


= ac-bd + (ad+bc)i





playing around with imaginary equations produces great looking fractals. If you want more info about imaginary figures (also known as complex figures) then e-mail me at gamesplayerbowditch@btinternet.comIs (square root of x) to the second power = x an identity (true for all non negative values of x and why?
Yes!





--- Although the simplified equation is x, we should not forget the real equation. In choosing all possible values of x, we look at the original equation and not the simplified ones. Since you can never have negative values inside the squareRoot symbol(unless you want to yield imaginary numbers), x should always be a positive number(zero included), hence {X|X%26gt;=0}

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