Question

find the number of digits in the square root of each of the following numbers without any calculation. 49
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Answer 1

Answer:

Answer

If the number of digits of a number is even, then its square root will have half  (whole number) of the number of digits.

If the number of digits of a number are odd, then its square root will have half (nearest greater whole number) of the number of digits.

i) 64

   The number of digits is 2 i.e. even.

   Therefore, there is only 1 digit in the square root of 64.

ii) 144

   The number of digits is 3 i.e. odd.

   Therefore, there are (1.5 =) 2 digits in the square root of 144.

iii) 4489

    The number of digits is 4 i.e. even.

   Therefore, there are 2 digits in the square root of 4489.

iv) 27225

    The number of digits is 5 i.e. odd.

    Therefore, there are (2.5=) 3 digits in the square root of 27225.

v) 390625

    The number of digits is 6 i.e. even.

    Therefore, there are 3 digits in the square root of 390625.