An algebra problem by Sakanksha Deo
2 2 2 2 2 . . . . . . = ?
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1 solution
You can try a different version of this problem here . nested radicals......
I did the same its a nice ques
How exactly does it become 2x=x squared from all of those roots? Why is it 2x on the left side?
or x=0 which isn't listed, so x=2.
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x can never be 0, since the square root of a positive number is always positive..
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Touché, thank you for that.
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@David Holcer – You are always welcome.....try other questions of my set.
You're process of solving for x is flawed. Check your answer. Try taking the square root of 2, then the square root of that number, then the square root of that number.... You end up with a number that infinitely approaches 1.
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I think such infinite series cannot give you exact answers by any process.....its more of a rounding fingure...we just find number to which the answer is most closest to.
You would be right except it is not asking for the square root of the square root of ... Of the square root of two. There is a 2 under every radical. The correct process is to take the square root of two, then double it, then square root, then double, ad infinitum, which gives 2 .
Let,
2 2 2 2 . . . . . . . = x
Squaring both sides,
2 2 2 2 2 . . . . . . . = x 2
2 x = x 2
x = 2