Question

$\sqrt{12 + \sqrt{12 + \sqrt{12..........} } }$
what is the answer ?????????

Answer 1

Explanation:

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

Answer 2

4 is the answer. .... ....