Answer:

The square root of 12

3 squared is 9

4 squared is 16

so the square root of 12 is around half way between 3 and 4 so lets guess 3.5

Now use the Babylonian method to find the exact answer.

take 12 and divide it by the latest guess 3.5 =3.42857142857. Add this to 3.5 and divide the answer by 2.

then add the answer which 3.46428571429

use this answer and repeat the calculation

(12/3.46428571429 + 3.46428571429 )/2 = 3.4641159043

once more 3.46410161517 and once more 3.46410161514

so this is the square root of 12.

The square of 12

Write two twelves vertically and a LINE underneath

12

12

…

24

The 2,s are in what we call the units column.

The 1's are in the the tens column.

Times the 2 x 2 = 4

Then times the lower 2 by the 1 of the upper 1

=2

We are left with 24 under the line as above

Next write 0 under the units column under the 24 already WRITTEN down.

Times the 1 in the tens column by the 2 sbove Times the 1 in the tens column by other 1 in the number 12 above = 1. Write these numbers under the 24 already written down.

12

12

……

24

120

Add up the columns

144 is the answer to 12 x 12.

Now you can see 10 x 12 = 120

and 2 x 12 = 24

This is how the above sum works.

Add 24 and 120 and you get 144.

Or learn the 12 times table

One twelve is twelve. Two twelves are twenty four. Three twelves are thirty six. Four twelves are forty eight. Five twelves are sixty. Six twelves are seventy two. Seven twelves are eighty four. Eight twelves are ninety six. Nine twelves are one hundred and eight. Ten twelves are one hundred and twenty. Eleven twelves are one hundred and thirty two. Twelve twelves are one hundred and forty four.

Write this down and watch the end number including 0 for no twelves.

0

12

24

36

48

60

72

84

96

108

120

132

144

Notice the left hand

Notice the right hand side units count in 2's and the left in 1′s

0,2,4,6,8,0,2,4,6,8,0,2,4. Right column

0,1,2,3,4,6,7,8,9,10,12,13,14 Left colomn

Notice 5 and 11 are missing in the left column.

This is the only table where this happens

So by WRITING this out the end numbers are 14 and 4. Add these together and you get 144 which is 12 x 12 or 12 squared.

Mike