Question

Find the number of digits in the square root of the number 2065702500 .​

Answer 1

Answer:

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Answer 2

Given : 2065702500 .

To Find : number of digits in the square root of the number  

Solution:

Process to find Digit in square root of any number

Start making group of 2    from right side   till all digits exhaust or 1 digit remains

if 1 digit remain make a group of that digit

Now count the number of groups  

Number of groups determine digits in square root of number

(AB)(CD)(EF)  = 3 groups => √ABCDED has 3 digit

 (B)(CD)EF)  = 3 groups =>     √BCDED has 3 digit

(20)(65)(70)(25)(00) = 5 groups

there are 5 group  hence 52 digits in square roots of 2065702500

√ 2065702500 = 45,450  ( 5 digits ) verified

General rule :

Digits in square roots of a number   =  n/2  if n is even

= (n + 1)/2  if n is odd  

Another method

100000000 < 2065702500 < 10000000000

10000² <    x²      <  100000²  

x²  = 2065702500

=> x = √2065702500

10000 < x  < 100000

Hence x has 5 digits

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