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A4. Real numbers : surds.

Numbers such as sqrt2 or sqrt3 are called surds. In fact any number which can be written using a square root symbol is called a surd. These are all surds:

sqrt77, 3+sqrt2, 101-sqrt61, 5/sqrt3...

Some surds can be simplified a little:
sqrt12=sqrt(3 x 4)=sqrt3 x 2=2sqrt3
sqrt96=sqrt(6 x 16)=sqrt6 x sqrt16=4sqrt6


Some numbers can be simplified further so that they no longer have a square root. In this case they are not called surds:

sqrt4=2
2sqrt25=2 x 5=10

You can do arithmetic with surds:
sqrt77 x sqrt77=77, sqrt3 + sqrt3=2sqrt3, 5sqrt7 - 2sqrt7=3sqrt7



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