 The symbol is called a.  b is called the.  n is called the.  if n is, and if n is.  We can take an root of a negative number, but we cannot take an root of a negative number. radical radicand index odd even odd even

 1.  2.  3.

 For all, a, b,, and:  1.  2.  This theorem works in reverse as well. We can use it to simplify radicals or to combine two radicals. Just remember that in order to combine two radicals they MUST have the same index!

 4.  5.  6.

 Remember, we never want a in the denominator. So, we need to rationalize it! radical

 7.  8.

 For all b and, and m and n positive integers,   9. Simplify.

 For k and m integers and all b and,   10. Simplify.

 To simplify a root with variables we divide the exponent on the variable by the index. The quotient is the exponent on the variable the radical, and the remainder is the exponent on the variable the radical. inside outside

11.12.

13.14.

15.16.

17.18.