Numerical methods- Show that f(x)=0 has a root near to x=5

Here's the question:
When I read it, I subbed in 4.9 and 5.1
My question is, how do I know which numbers to sub in or why 5 was subbed in this case ?

Also, is the graph of y= x^ 1/2 here correct ?

Here's the question:
When I read it, I subbed in 4.9 and 5.1
My question is, how do I know which numbers to sub in or why 5 was subbed in this case ?


Also, is the graph of y= x^ 1/2 here correct ?

I would say not; there seems to be a fairly strong consensus that $\sqrt{x}$ should be taken as always meaning the +ve square root only. (I am personally always a little uncomfortable about this, due to 3rd year university complex analysis courses that always give me a strong sense of "it depends", but for A-level my understanding is it's the +ve root).