Roots of real numbers and radical expressions
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Roots of Real Numbers and Radical Expressions PowerPoint PPT Presentation


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Roots of Real Numbers and Radical Expressions. Definition of n th Root. For any real numbers a and b and any positive integers n , if an = b , then a is the n th root of b . ** For a square root the value of n is 2. radical. index. radicand. Notation.

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Roots of Real Numbers and Radical Expressions

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Roots of real numbers and radical expressions

Roots of Real Numbers and Radical Expressions


Definition of n th root

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

Notation

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


Simplify

Solution: = 3

Simplify

To simplify means to find x in the equation:

x4 = 81


Principal root

Principal square root

Opposite of principal square root

Both square roots

Principal Root

The nonnegative root of a number


Summary of roots

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

Examples


Examples1

Examples


Taking n th roots of variable expressions using absolute value signs

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.


Examples2

Odd

Odd

Even

Even

Even

Even

Examples


Roots of real numbers and radical expressions

Odd

Even

Even

Even

Even

Odd

2


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