A1Side

Multiplying and dividing radicals makes use of the "Product Rule" and the "Quotient Rule" as seen at the right. The "n" simply means that the index could be any value. Our examples will be using the index to be 2 (square root).

statement
Multiplying Radicals: When multiplying radicals (with the same index), multiply under the radical, and then multiply in front of the radical (any values multiplied times the radicals).

expin1
mu math1
ANSWER: mu math1c
 

Multiply the values under the radicals. mu math1a
Then simplify the result. mu math1b

 

expin2
mu math2
ANSWER: mu math2c
 
Multiply out front and multiply under the radicals.mu math2a
Then simplify the result.
mu math 2b


Product Rule

rule n multwhere a ≥ 0, b≥ 0

"The radical of a product is equal to the product of the radicals of each factor."


Quotient Rule

rule n div
where a ≥ 0, b > 0

"The radical of a quotient is equal to the quotient of the radicals of the numerator and denominator."

expin3

mu math3
ANSWER: mu math3c
 
Multiply under the radicals. mm3aa
Then simplify the result. mu math3b



expin4
mu math4
ANSWER: mu math4c
 

Distribute across the paretheses. Remember there is an implied "1" in front of 4aa.
mu math4a
Then simplify the result. mu math4b


expin4
d
ANSWER: radex5c
 

Use the distributive property to multiply. Combine like terms.
radex5a


expin4
radex6
ANSWER: dnranex6aans
 

Use the distributive property to multiply. There are NO like terms to be combined.
dmradex6a



statement
Dividing Radicals: When dividing radicals (with the same index), divide under the radical, and then divide in front of the radical (divide any values multiplied times the radicals).

expin5
mu math5
ANSWER: mu math5c
 
Divide out front and divide under the radicals. mu math5a
Then simplify the result. mu math5b


expin6
mu math6
ANSWER: mumath6c
 

This fraction will be in simplified form when the radical is removed from the denominator. You need to create a perfect square under the square root radical in the denominator by multiplying the top and bottom of the fraction by the same value (this is actually multiplying by "1"). The easiest approach is to multiply by the square root radical you need to convert (in this case multiply by rad5).
mumath6a You have just "rationalized" the denominator!

 

divider

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