Question

i. If a number has 'n' digits, then the number of digits in the square of the numbers​

Answer 1

Given :a number has 'n' digits,

To Find : number of digits in the square of the numbers​

Solution:

Number with 1 Digit  

1  ≤ x  <  10²

1   ≤ x² < 10²

1 ≤  x² < 100

Hence x² is 1 or 2 digit

a number x  has '1' digits  then square has 1 or 2 digit

Number with 2 Digit  

10  ≤  x  <  100

10² ≤ x² < 100²

10² ≤ x² < 10000

Hence x² is 2 or 2 digit

a number has '2' digits  then square has 2 or 3 digit

Number with n Digit  

1000..(n-1) times 0  ≤  x  <  1000 (n times zero)

1000.. 2(n-1)  times 0 ≤ x² <  1 000......  (2n times zero)

1 + 2(n- 1) = 2n-1 digits  

1 + 2n = 2n + 1 digit

2n-1 digits  ≤  x² < 2n + 1

Hence number of possible digits in x²   are  2n-1  or 2n

Hence a number has 'n' digits  then square has 2n-1  or 2n  digit

if a number has 'n' digits, then the number of digits in the square of the numbers​  are  2n-1  or 2n

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