Raymond B. answered • 05/04/20
Math, microeconomics or criminal justice
17
17x17 = 289
most people use a calculator
but there is a long hand way to do it
you could also just try a few guesses
15 x 15 = 225
20x20 = 400
you want something in the middle, but closer to 15
17 is the next integer to try and it works
another clue is you need a number ending in 3 or 7 to get 9 as the last digit for the squared term
3x3=9 7x7=49
13 x 13 is 169
17x 17 = 289
Here's another method
separate 289 by pairs of digits
into 2 89
pick the largest integer which squared is = or less than 2. That's 1
subtract 1 from 2, to get 1, bring down with the 1 the next pair of digits, to get 189
double the 1, to get 2
look for the largest integer x such that 2 in the tens position and x in the one's position multiplied by x is less than or equal to 189
27 x 7 = 189
You write it sort of like long division, with the 1 and 7 appearing where a quotient normally appears'
and the 27 as a divisor of sorts
The advantage of this method is when you don't have a calculator, and also when the answer is not an integer. Had you asked the square root of 290, you could have continued to bring down pairs of zeroes, and continued to get the square root as 17.03 rounded to two decimal places or you could bring down as many pairs of zeroes as you want decimal places.
