LAWS OF RADICALS

 

 

Definition of a radical

product of two radicals

quotient of two radicals

Like index and exponent

Radicals Main Menu

 

 

Property in Symbolic form Property stated in words Example

Definition:

A radical represents a fractional exponent in which the numerator of the fractional exponent is the power of the base and the denominator of the fractional exponent is the index of the radical.

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Definition of a radical

product of two radicals

quotient of two radicals

Like index and exponent

Radicals Main Menu

 

 
Property in Symbolic form Property stated in words Example

Product:

The nth root of a product is equal to the product of the nth  root of each factor.

 Note: the indices must be the same.

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Definition of a radical

product of two radicals

quotient of two radicals

Like index and exponent

Radicals Main Menu

 

 
Property in Symbolic form Property stated in words Example

Quotient:

The nth  root of a quotient is equal to the nth  root of the numerator divided by the nth  root of the denominator.

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Definition of a radical

product of two radicals

quotient of two radicals

Like index and exponent

Radicals Main Menu

 

 
Property in Symbolic form Property stated in words Example

Exponents:

 

caution: beware of negative bases when using this rule. See examples.

 

 

caution: beware of negative bases 


This answer is negative because the exponent is odd.


This answer is positive because the exponent is even.

 

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Definition of a radical

product of two radicals

quotient of two radicals

Like index and exponent

Radicals Main Menu