Question

Plz find decimal expansion of root 5 up to 5 decimal places

Answer 1

We know that 22 = 4 < 5 < 9 = 32 
Taking positive square roots we get
2 <  √5 < 3.

Next, (2.2)2 = 4.84 < 5 < 5.29 = (2.3)2
Taking positive square roots, we have
2.2 < √5 < 2.3

Again, (2.23)2 = 4.9729 < 5 < 5.0176 = (2.24)2
Taking positive square roots. we obtain
2.23 < √5 < 2.24
Hence the required approximation is 2.24 as (2.24)2 is nearest to 5 than
(2.23)2