Indices

“nth” nth Root of a Real Number The "nth Root" used n times in a multiplication gives the original value " nth ? " 1st,  2nd,  3rd,  4th,  5th,  …,  nth,  …  Instead of talking about the "4th", "16th", etc, if we want to talk generally we say the “nth”

Just like the square root is The nth Root 2 Just like the square root is used two times in a multiplication to get the original value.

used three times in a multiplication to get The nth Root 3 The cube root is used three times in a multiplication to get the original value.

used n times in a multiplication to get the original value. The nth Root n The nth root is used n times in a multiplication to get the original value.

. Let a be a real number and n be a positive integer. If there exists a real number r such that rn = a Then r is called the nth root of a. The nth root which has the same sign as a is denoted by

The nth Root Symbol This is the special symbol that means "nth root", it is the "radical" symbol (used for square roots) with a little n to mean nth root.

42 = 16 is the second root or square root of 4 16

(-42) = 16 -4 is also a square root of 16 It is denote by

-7 and 5 are the third roots or cube roots of 53 = 125 (-7)3 = -343 -7 and 5 are the third roots or cube roots of -343 and 125 respectively.

-3 and 3 are the fourth roots of 81. 34 = (-3)4 = 81 -3 and 3 are the fourth roots of 81. Positive 4th root Negative 4th root

Positive nth root Negative nth root when a  0 and n is an even integer. There are two real nth roots of a. Positive nth root Negative nth root

that when a  0 and n is even, Note that when a  0 and n is even, is undefined in the real number system. Thus, undefined

a = 0 a  0 a  0, n is odd number Conclusion of nth roots of a or is positive number a  0 is negative number a  0, n is odd number

Ex1 Find the values of the following. Write 64 in the form r3

Write 625 in the form r4 is also a 4th root of 625, but only present the positive 4th root.

Write -8 in the form r3