Question

find the value of root 5 upto 3 decimal places

Answer 1

hello friend !

√5 = 2.2360679774997896

well that was a calculator answer
let me show how to find it manually

the closest perfect square near 5 is 4
clearly our first no. is

2

also 5 - 2^2 = 1
put two zeroes we have 100

double our first answer which was 2
now it is 4

now 42 ×2 is 84 while 43 ×3 is 129 ( greater than 100 that we have earlier)
now our no. is

2.2 as we multiplied 42 ×2

100-84 =16
add 2 zeroes =1600

double the previous no. 2.2
now it is 4.4

now 443×3 is 1329
while 443×4 is greater than 1600
now our no. is 2.23

1600-1329 = 271 add 2 zeroes
27100

double the previous no. 2.23
now it is 4.46
now 4466 ×6 is 26976
while 4467×7 is greater than 27100

hence our answer is 2.236

hope it helps
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