Introduction
Happy New
Year to our readers! I wish this year
will be a fruitful one for everybody.
Today, I
will illustrate how to calculate square roots by hand, using 54 756 as
an example. It is similar to long
division, but has some modifications.
Solution
Starting
from the right, pair up the digits.
2×2 =
4 is the nearest perfect square to 5. Subtract
and bring down the next two digits, giving 147.
Double the digit
2
to get 4. Think: ? × 4?
gives 147 or nearest possible value. We have 3×43 = 129.
Subtracting
and bringing down the next two digits gives
1856. Replicate the digit 4 on
the left and double the digit 3, giving
46.
Now think: ? × 46?
gives 1856 or nearest possible value. It turns out that 4 × 464 gives exactly 1856.
We are done! The square root
of 54 756 is
234.
How does it work?
This relies on the algebraic identity (10a + b)² = 100a² + 20ab + b², the right-hand expression is equal to 100a² + (20a + b)b. For example, at stage 4, we have a = 23, b = 4 and (20a + b) = 464.
Did you
learn something today?
