What he's talking here is correct and possibly trying out the SQR function on a calculator. That's what his original question was, and this video wasn't there.
Repeated keypresses of the SQR finally results in 1.
Each time the SQR is pressed the calculator does the square root , which is raising the number to the power of 1/2 or 0.5. If you press it three times effectively the original number is raised to the power of (0.5)^3 or 0.125
Press it 10 times then the number will be raised to the power of (0.5)^10 =1/1024 which is 0.0009765625
Press it 25 times and the power will be .0000000298023224
With further repeats this power gets smaller and smaller and reaches 0 (at least the calulator's machine computational limit of 0)
Any Number raised to the Power of 0 is 1 - and that's why the answer is 1.