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Surds are numbers left in 'square root form' (or 'cube root form' etc). They are therefore irrational numbers. The reason we leave them as surds is because in decimal form they would go on forever and so this is a very clumsy way of writing them.
This animated video explains that surds are the roots of numbers that are not whole numbers. An example shows why surds are not written out as decimals because they are infinite decimals. Rules of working with surds are outlined and it is demonstrated how they can be simplified and rationalised.