Roots of Real Numbers and Radical Expressions

Roots of Real Numbers and Radical Expressions

Definition of nth Root For any real numbers a and b and any positive integers n, if an = b, then a is the nth root of b. ** For a square root the value of n is 2.

radical index radicand Notation Note: An index of 2 is understood but not written in a square root sign.

Solution: = 3 Simplify To simplify means to find x in the equation: x4 = 81

Principal square root Opposite of principal square root Both square roots Principal Root The nonnegative root of a number

Summary of Roots no real roots one + root one - root even one real root, 0 one + root no - roots no + roots one - root odd

Examples

Taking nth roots of variable expressions Using absolute value signs If the index (n) of the radical is even, the power under the radical sign is even, and the resulting power is odd, then we must use an absolute value sign.

Odd Odd Even Even Even Even Examples

Odd Even Even Even Even Odd 2

Roots of Real Numbers and Radical Expressions