Question

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

Answer 1

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