Question

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

Answer 1

I shall give you 2 ways to solve the problem.

Method 1 is explained above, in the previous answer.
let,
x= √12+√12+√12+√12......
( i have written five √12)

Now, if you remove one √12, will the question change??

No. Because infinite - 1 = infinite.
Removing one √12 will not change the answer.
ie,
x = √12+√12+√12+√12....( only four √12)
Now, we replace,
the last four √12+√12+√12+√12..... as x

Now, we get x=√(12+x)
Take square, as do as explained in the above image, to get answer, 4.

THIS IS THE METHOD TO SOLVE THESE PROBLEM. REPLACE ALL THE LAST ROOTS BY 'x'.

METHOD 2.
Its an easy method. Find the number inside root. Here, it is 12. Now, write the number as n(n+1) . That is, express number as multiples of 2 consecutive numbers. Here, 12= 3 *4. The answer is the number (n+1) , here 4.

Another example???
To find √2+√2+√2+√2....
put x = √2+x , and solve.
OR, 2 = 1 * 2, express 2 as product of 2 consecutive numbers, here 1 and 2. The answer is (n+1) , ie, 2.

Hope this helps.
Jusk ask a question if there is anything you dont understand.