find the positive square root of i) 12-4√5 with solution please
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find the positive square root of i) 12-4√5 with solution please
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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