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Question

Find the square root of 23


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Solution

Find the approximate square root of 23

First find the nearest perfect square to 23 .

25 is the nearest perfect square around 23

Now given terms can be written as

23=25-2

=25121-22512

We know that when when the term is in this form (1+x)n where x is so less than 1 then it is written as (1+nx)

Then according to above condition

23=51-225×12

=51-125=5-15=5-0.20

23=4.80

Hence the square root of 23 is approximately equal to 4.80


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