The eight girls I have been teaching math in high school are very smart. The twin sisters Ariella and Briella certainly are. For example, one time they challenged me to choose a square number between 100 and 10000. They would then immediately say the root of that number. I took the number 9604 and indeed Ariella immediately said 9 and Briella then 8. The answer is indeed 98.
This is how they do it:
Ariella knows all squares from 1 to 9 by heart: 1, 4, 9, 16, 25, 36, 49, 64, 81
Briella knows the last digits of the squares from 0 to 5 by heart : 0, 1, 4, 9, 6, 5
As soon as the girls hear the number they do the following:
Ariella subtracts the last two digits from the number (9604 becomes 96). She sees that 81 is the lowest square that is less than or equal to 96. 81 is the square of 9, so she calls out "9". Next, she calculates 9 × (9 + 1) = 90. Because 90 is smaller than 96, she raises her thumb. By doing this, she sends a signal to Briella.
Briella meanwhile looks at the last digit of 9604 (= 4). She knows that 4 is the last digit of the square of 2. But she notices that Ariella has her thumb up. She calculates 10 minus 2 = 8. She calls out "8".
Together they give the correct answer 98.
See below how this is done with other numbers.
Choose a square number between 100 and 10000: ≪<144>≫
