A number with 100 digits is given. The first two digits of that number are 2 and 9. How many digits has a square of that number?
Answers
Answer:
A number with 100 digits is given. The first two digits of the number are 2 and 9. How many digits has a square of that number?
When we multiply an ‘n’ digit number with an ‘n’ digit number the product consists of either 2n digits or 2n-1 digits.
A single digit number 3 has its square 9, which is still a single digit number.
A single digit number 4 has its square 16, which is a 2-digit number.
A two digit number 31 has its square 961, which is a 3 digit number.
A two digit number 32 has its square 1024, which is a 4 digit number.
A three digit number 316 has its square 99856, which is a 5 digit number.
A three digit number 317 has its square 100489, which is a 6 digit number.
As you must have guessed, a 100 digit number starting with 29… will always have its square consisting of 100+100–1 = 199 digits, no matter what the digits beyond 29 are!
Square root of 10 is 3.162277660168379….
Now you will know the connection between Square root of 10 and the number of digits in Squares of 3, 31 and 316 (and so on …). You will also know as to why the number of digits in squares of 4, 32 and 317 is twice the number of digits in 4, 32 and 317 (and so on …) respectively.