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  • A surd is a square root which cannot be reduced to a whole number. For example, square root of 4 = 2 ( is not a surd, as the answer is a whole number. But square root of 5 ( is not a whole number. You could use a calculator to find that square root of 5 = 2.236067977 ( but instead of this we often leave our answers in the square root form, as a surd.
  • You need to be able to simplify expressions involving surds. Here are some general rules that you will need to learn.
  • square root of ab = square root of a x square root of b (
  • square root of a x square root of a = a (
  •  If you are adding the square root of a to b it is not the square root of a+b.


Simplify square root of 12 ( square root of 4 x square root of 3 ( square root of 3 (

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Probability and tree diagrams

Tree diagrams allow us to see all the possible outcomes of an event and calculate their probability. Each branch in a tree diagram represents a possible outcome.

If two events are independent, the outcome of one has no effect on the outcome of the other. For example, if we toss two coins, getting heads with the first coin will not affect the probability of getting heads with the second.

   A tree diagram which represent a coin being tossed three looks like this :

image: tree diagram and probabilities (

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