Take 87 as a starter. To be able to use this method, you need to know basic squares and roots and you're looking for the nearest whole number square below 87 in this case.
Which is 9 x 9 = 81.
Now, what's the difference between 81 and 87?
It's 6, yes? Double the 9 and put it below the vinculum so 6 over 18 = 1 over 3 = 0.33 recurring. All up then, the square root is roughly 9.333 etc.
How much is it exactly, by calculator? 9.327 . Ball park. Not far away.
Let's do one more. Square root of 43. Nearest is 6 squared. Difference is 7.
So, 7 over 12 is our fraction. Ballpark answer is 6 point just over 5, maybe point 55 or 56.
And by calculator = 6.557. Try a few of your own.
Here's another quick one:
ReplyDeleteAny number (N) ending in one half (n+0.5) may be squared easily:
First 'remove' the half, leaving the integer (n), then
N squared = n times (n+1) + 1/4
Examples
3.5 squared = 3 x 4 + 0.25 = 12.25
6.5 squared = 6 x 7 + 0.25 = 42.25
11.5 squared = 11 x 12 + 0.25 = 132.25
My method for sqrt(43). It must be about half way between 6 and 7. Ans 6.5
ReplyDelete