This nested radical Involving Subtraction Will break your brain

Added: 2026-05-05

[00:00:02]Hello, let us solve this uh problem and I call it the nested subtraction. Why is it nested? Because as you can see there is a radical under a radical under a radical and so on infinite radicals under a radical. So, we have here nested and we call it subtraction. So, the radicals are actually subtracted. So, the first thing we need to do is we will analyze it. So, we as I have said in my previous video, we have here since the expression it goes on forever, the part inside the first square root is exactly the same as the whole thing.

[00:00:43]As you can see they're just So, the first the one inside the first square root is just the same as the second and so on and so forth. So, it just repeats and repeats. So, the trick here is we will let X equal to the square root of 12 minus X.

[00:01:02]So, if we let uh X equal to the square root of 12 minus X, it's actually the same because this is minus X 12 minus X and the next one would be the minus X and so on. So, we can let X equal to square root of 12 minus X and then we will solve for X. What we will do is we will square this.

[00:01:25]We will square it and it would become X squared and we cancel the radical and what is left is 12 minus X. Once we have this, we will write it like this one. It becomes a quadratic equation. X squared and then we will factor X squared plus X minus 12. The factors are X plus 4 and X minus 3.

[00:01:50]Here we have we will equate the two factors to zero. So, this would become here X equal to negative 4 and this one would become X equal to positive 3 and the final answer is X equal to 3 because we don't want a negative root. We only want the positive root. So, therefore the final answer is X is equal to 3.

[00:02:14]Uh if you have some questions, leave a comment below.