question_answer 1)

                Find the number of digits in the square root of each of the following numbers (without any calculation): (i) 64                                      (ii) 144                                   (iii) 4489                               (iv) 27225 (v) 390625.

Answer:

                (i) 64 Number (n) of digits in 64 = 2 which is even. \[\therefore \] Number of digits in the square root of \[64=\frac{n}{2}=\frac{2}{2}=1\]. (ii) 144 Number \[(n)\] of digits in 144 = 3 which is odd. \[\therefore \] Number of digits in the square root of \[144=\frac{n+1}{2}=\frac{3+1}{2}=\frac{4}{2}=2\]   (iii) 4489 Number (n) of digits in 4489 = 4 which is even. \[\therefore \] Number of digits in the square root of \[4489=\frac{n}{2}=\frac{4}{2}=2\]. (iv) 27225 Number \[(n)\] of digits in 27225 = 5 which is odd. \[\therefore \] Number of digits in the square roots of \[27225=\frac{n+1}{2}=\frac{5+1}{2}=\frac{6}{2}=3\]. (v) 390625 Number \[(n)\] of digits in 390625 = 6 which is even. \[\therefore \] Number of digits in the square root of \[390625=\frac{n}{2}\,=\frac{6}{2}=3\].