The root of a number is that
number which, when multiplied by itself so many times, equals the given number;
the 'square' root of 4 is 2, ie 2 X 2 = 4, and this is written
= 2.
Similarly the 'cube' root of 8 is
2, ie 2 x 2 x 2 = 8, and
= 2 etc. Note the little 2 in the sign for square root is
normally omitted so that
signifies the square root.
Numbers like 4, 16 and 25 are called 'perfect' squares because their square roots are whole numbers, thus
etc.
The following should be memorised as they can often be very useful.
For example
It is always worth checking to see if the number left after dividing by 2, 3 or 5 is a perfect square.
The square root of a number
expressed in the index notation is found by dividing the index by 2, thus
and
, and so on. Similarly
etc. Should the index be an odd number, it must be made into
an even number as follows.
The constant
term 'p' occurs in many calculations; 'p'
has great significance in mathematics and is the ratio of the circumference to
the diameter of a circle. p can be
taken to be 3.14 or 22/7. The error in taking
as 10 is less than 1.5 per cent and is acceptable here.
can be taken as 0.32 and
as 0.16 (the error in calling this 1/6
is really somewhat too high).
= 0.16 is particularly useful.
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