Question 398046
x(x-7) must have positive values, or zero, in order the square root of it to be a real number.
That happens in the following cases:
(i)    x>=0 and x-7>=0
(ii)    x<=0 and x-7<=0
The zeros of x(x-7) are 0 and 7 
the conditions (i)  is valid when x>=7 
the condition (ii) is valid if x<=0
--------------0------7---------------
         + ~~~~~~~~~~~       - ~~~~~~~~~~        +      
So the intervals for sqr[x(x-7)] to be a real number are (-&#8734; ,0] and [7,+&#8734;)