Roots of Real Numbers and Radical Expressions

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Presentation transcript:

Roots of Real Numbers and Radical Expressions

** For a square root the value of n is 2. 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.

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

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

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

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

Examples

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.

Examples Even Odd Even Odd

Even 2 Odd Odd Even