Today,
I will show you a well-known method in order to find a square root on
your own, without any help of a calculator. This is one of the
typical piece of knowledge which is being forgotten and being left to
teach, due to the fact that calculators and computers solve them.
Certainly, I already know that
it is quite easy, but it is the previous path towards my next post.
It starts typing in the number
under the radical and proceed as follows:
1) The figures are split up
into groups of two from right to left.
2) The
first group on the left is taken, which is 83.
Now,
it is necessary to think about an integer number that multiplies by
itself becomes 83 or
nearly
83
by default,
and
to take this number away from 83.
9
is the number,
since
92 =
81.
3)The following set of
numbers is 24 and it is lowered. Its is found the double of the root
that hasbeen calculated previously and it is located below 9 x 2 = 18.
4) Now, let's separate with a
point the last figure on the right, and divides what remains on the
left between double root that has been found beforehand, or what is
the same: 22:18 = 1
5) The
number 1 that has been obtained is placed on the right of the double
of the root, resulting in 181. Then a multiply sign is located after
181 and the number one after this multiply sign. Now the calculation
181*1 = 181 is done and this result is subtracted the number 224, on
the left side.
6) The number
1 rises where is placed the root
7) As there are no more groups of
digits to lower in the filing of the square root, the operation is
complete.
Then the root square of 8324
is 91 and the remainder 43.
8)
Checking:
912
=
8281
8291 + 43 = 8324.
9) Now,
if you want to get it
with
decimals is need to add as many pairs of zeros whatever decimal at
the end result. For example, if you want to get the root with two
decimal places, it is necessary to place a comma after the 8324 and
four zeros.
Afterwards,
the procedure is like the previous steps.
Therefore, the square root of
8324 with two decimal places is 91.23 and the remainder would be
1.0871.
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