# Mathematics for the RAE

### Roots of numbers

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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