s²=5 , so we look for the nearest squares, one less than 5 and the other greater.
First it would be perfect squares, which means 4=2² and 9=3²
4 < 5 < 9 so 2 <√5 < 3
now we'll do the same with the numbers with tenths, but to speed up we don't check them all. We do estimation for the square root knowing that it must be between 2 and 3
5 is close to 4 then 9, so I estimate 2.3 for its square root
(2.3)² = 5.29 - it is close but more then 5 so I look for less number then 2.3
(2.2)² = 4.84 - it is also close and less then 5 so:
4.84 < 5 < 5.29 therefore 2.2 < √5 < 2.3 and:
5 - 4.84 = 0.16 ; 5.29 - 5 = 0.29
0.16 < 0.29 means the √5 is closer to 2.2 then 2.3
So the √5 rounded to the nearest tenth is 2.2
Of course is much easier if you can use the calculator. Then you have:
√5 = 2.2360679... ≈ 2.2 {because 3<5}
:)