Question

26. September 9, 1981 (9/9/81) was a square-root year date because both the

month and the day are square roots of the last two digits of the year.
How many square-root dates will there be during the 21st century?

Answer 1

There will be no square-root dates like 9/9/81 in the 21st century because there are no valid months and days corresponding to the square roots of perfect squares over 9 within the 21st century.

Step-by-step explanation:

The question asks how many square-root dates will there be during the 21st century. A square-root date is when both the month and the day are square roots of the last two digits of the year. To find these dates, we would need perfect squares for the last two digits of a year that also correspond to the months and days that are their square roots.

There are three perfect squares that can represent months: 1 (January), 4 (April), and 9 (September). For 1 and 4, the corresponding years would be 01 (2001) and 16 (2016) because the square roots of 1 and 4 are 1 and 2, respectively. For the number 9, the corresponding years would be 81 (2081), because the square root of 9 is 3.

Hence, there are three square-root dates in the 21st century: 1/1/01, 2/2/04, and 3/3/09 (assuming the pattern continues from the 20th century). However, there will be no square-root date like 9/9/81 in the 21st century because there are no months and days that correspond to the square root of any perfect square over 9 that would be a valid date within the century.

Answer 2

Step-by-step explanation:

A century has 100 years in it. months only has a max of 31 dates. The following years are perfect squares, 01,04,09,16,25,36,49 64,81,100

It will be 10 square root dates.