Find the square root of 23

We have to find the square root of 23.

Solution

First, let us find the nearest perfect square to 23.

25 is the nearest perfect square around 23

Now let us follow the given method

√23 = (25 – 2)½

25{(1 – 2/25) }½

=> 25½{1 – 2/25}½

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

5 (1 -2/25*1/2)

=> 5 (1 -1/25)

=>( 1- 5/25 )

=> ( 5 – 1/5)

=> (5 – 0.20)

=> 4. 80 is the square root of √23

Answer

√23 =4.80

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