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 how to find the value of √(√2+√2+√2+√... ?

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646
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avatar+4 

plese give me the steps to solve the question , thx

 Apr 10, 2015

Best Answer 

 #1
avatar+33666 
+13

An infinite number of √2's added together is infinite, so the square root of that is also infinite.

Is that what you really meant?

 

If, instead, you meant √(2*√(2*√(2*... then let x = √(2*√(2*√(2*...
 
Square both sides:  x 2 = 2*√(2*√(2*..., but if the right-hand side goes on forever then it is just 2x, so
 
x 2 = 2x
 
x = 2
.
 Apr 10, 2015

2+0 Answers

 #1
avatar+33666 
+13
Best Answer

An infinite number of √2's added together is infinite, so the square root of that is also infinite.

Is that what you really meant?

 

If, instead, you meant √(2*√(2*√(2*... then let x = √(2*√(2*√(2*...
 
Square both sides:  x 2 = 2*√(2*√(2*..., but if the right-hand side goes on forever then it is just 2x, so
 
x 2 = 2x
 
x = 2
.
Alan Apr 10, 2015
 #2
avatar+118724 
+5

Hi Alan,

Your alternate question and answer fascintates me every time.   

It is so simple yet so confusing (when seen for the first time)

I still get a minor buzz out of that question.  Mmm, I must have mathematics in my blood :)

 Apr 10, 2015

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