Question

without actually finding the square root of the number determine the number of digit in square root of a 2025 b 53361 c 271441

Answer 1

Given : 2025

53361

271441

To Find   : determine the number of digits in the square root of. 2025

Solution:

2025

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

  2025

 (20)(25)

there are two group  hence 2 digits in square roots of 2025

√2025 = 45  ( 2 digits ) verified

General rule :

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

= (n + 1)/2  if n is odd  

53361   = (5)(33)(61)   - 3 digits    √53361 =  231  verified

271441 = (27)(14)(41)   - 3 digits     √271441=  521   verified

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Answer 2

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