What is the value of √20 + √20 +√20 + √20 + ...?
It's not "the square root of {20} plus the square root of {20} plus the... " but "the square of {20 plus the {square root of 20 plus the... }}"
It's to show it on the computer, sorry.
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Assume the answer is x. Now think about: what will happen, if we were to add 20 to x, and then take the square root? Well, we get a number of exactly the same 'description' as the original x. That is, x. In other words, we just constructed the equation x = √(20+x).
With the standard issues concerning radic equations about signs in mind, this can be (carefully) squared into
x^2=20+x
x^2 - x - 20 = 0
x = 5.
(The negative root is obviously false).
If its the square of 20 it would be 400 and the square root of 20 is 4 on the square root of 5. (sorry idk the square root symbol) So the answer would be infiniti, I mean it would be multiples of 400 plus multiples of 4 on the square root of 5 (8 on the square root of 5, 12 on the square root of 5 and so on).
Hope this answers ur question?
sqrt(20 + sqrt(20 + sqrt( 20 + ...
I'm not sure if the sum to infinity of this exists.
plug it into your calculator. . . your explanation is kind of foggy