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  A surd is a square root which cannot be reduced to a whole number.

  For example,v4 = 2 is not a surd. But v5 is not a whole number.

  You could use a calculator to find that 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.

  Two surds are equivalent if they express the same number:


  You can simplify surds in this way:



  Or you can use fraction indices: