Finding Square Root without a table
You are given the task of finding the
square root of a number that is NOT a
perfect square.
Find the perfect square just below and
above your number. Now take the square
root of those two numbers.
Place the sign for ´LVDSSUR[LPDWHO\ equal
Example:
Evaluate
176
196 14
196 14
176
176 |
169 13
169 13
WRµDIWHU\RXUDVVLJQHGQXPEHU
Since your number will need to be
between the square roots of your perfect
196 14
squares, place the smaller number after §
176 | 13.
Include a decimal point after it
169 13
Now look at the two perfect squares and
compute their difference. This number
will become the denominator of the
fraction you will use to compute the
decimal portion of your square root.
Now you must take the difference
between your number and the smaller of
the two perfect squares. That difference
is placed in the numerator of your
fraction. If your fraction does not easily
simplify, change one of the numbers so
you can simplify the fraction and change
that to a decimal easily.
Place that up where you have your
number, the ´LVDSSUoximately HTXDOWRµ
sign, the smaller perfect square followed
by a decimal. You have found a good
approximation for the square root of a
non-perfect square!!
196 ² 169 = 27
Notice that 14 + 13 = 27 as well
27
:HKDYHQ·WILJXUHRXWZKDWJRHVLQWKH
numerator, yet)
176 -169 = 7
7
This does not simplify easily but if I
27
change 27 to 28 I get the fraction 7/28,
which I know is ¼ or 0.25
196 14
176 13.25
169 13
So the answer is
176 | 13.25 If the
instructions say to round to the nearest
tenth, the solution woulGEH§