# 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 thus

Similarly the 'cube' root of 8 is 2, ie 2 x 2 x 2 = 8, and 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

The following should be memorised as they can prove to 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 √106 = 103 and √1012 = 106 and so on. Similarly √10-6 = 10-3 etc. Should the index be an odd number, it must be made into an even number as follows.

The constant term π occurs in many calculations has great significance in mathematics and is the ratio of the circumference to the diameter of a circle. π can be taken to be 3.14 or 22/7. The error in taking π2 as 10 is less than 1.5% and is acceptable here. 1/π can be taken as 0.32 and 1/2π can be taken as 0.16 (The error is calling this 1/6 is too high and should be avoided). The 1/2π = 0.16 is particularly useful to remember as the constant 1/2π is common in electronics.

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