How to Simplify Radicals:

  • First, collect all like terms in the radical

 

  • Arrange all the factors with like bases together

  • Determine what the index of the radical is.  The index is the small number cradled just above the "V" of the radical sign.  If no number is there, it is the square root, so the index is 2.
 

Since no number appears just above the "V", the index is 2.

  • For each base, raise as many factors of it as you can to the same power as the index.  Recall that , when you raise a power to a power you multiply the exponents, and when you multiply like bases you add the exponents.

 

  • All factors that have an exponent the same as the index come outside the radical sign (but NOT with the "outer" exponent that is the same as the index, and all other factors stay inside the radical sign.
 

 

Another example where the index is not 2:

 

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