Question

# √12+√12-√12+√12-√12 •••••••••••••• infinite

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Solution

## There is a really interesting math trick behind it. If you see a question like this take out the number inside it (in this case is 12) Take consecutive numbers such as: n(n+1)=12 Always remember that the answer is n+1 This is true because if you let the infinite nested radical function = x then realise that x is also also under the first root sign as: x=√12+x Then, squaring both sides: x2=12+x Or: x2−x=12 x(x−1)=12 Now let x=n+1 Then n(n+1)=12 With the answer to the infinite nested radical function (x) being equal to n+1 If you solve it you get n=3 and n+1=4 So, The answer is 4

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