square root of 5 by step by step
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1. Find the two perfect square numbers it lies between.
Ex: 5 lies between 2^2 = 4 and 3^2 = 9.
(i) Divide 5 by 2 = 2.5.
(ii) Average 2.5 and 2 = (2.5 + 2)/2 = 2.25.
(iii). Divide 5 by 2.25 = 5/2.25 = 2.222
(iv) Average 2.222 and 2.25 = (2.222 + 2.25)/2 = 2.236.
Verification:
2.236 * 2.236 = 4.99999 = ~5.
The square root of 5 = 2.236.
Hence proved.
Hope this helps! :)
Ex: 5 lies between 2^2 = 4 and 3^2 = 9.
(i) Divide 5 by 2 = 2.5.
(ii) Average 2.5 and 2 = (2.5 + 2)/2 = 2.25.
(iii). Divide 5 by 2.25 = 5/2.25 = 2.222
(iv) Average 2.222 and 2.25 = (2.222 + 2.25)/2 = 2.236.
Verification:
2.236 * 2.236 = 4.99999 = ~5.
The square root of 5 = 2.236.
Hence proved.
Hope this helps! :)
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