Intermediate Algebra Tutorial 39


Intermediate Algebra
Answer/Discussion to Practice Problems
Tutorial 39: Simplifying Radical Expressions

WTAMU > Virtual Math Lab > Intermediate Algebra > Tutorial 39: Simplifying Radical Expressions


 

checkAnswer/Discussion to 1a

problem 1a
 

ad1a1

*Use the prod. rule of radicals to rewrite

 
Note that both radicals have an index number of 5, so we were able to put their product together under one radical keeping the 5 as its index number. 

Since we cannot take the fifth root of ad1a2 and ad1a2 does not have any factors we can take the fifth root of, this is as simplified as it gets.
 

(return to problem 1a)

 


 

checkAnswer/Discussion to 2a

problem 2a
 

ad2a

 

*Use the  quotient rule of radicals to rewrite

*Square root of 49 is 7
 
 

Since we cannot take the square root of 5 and 5 does not have any factors that we can take the square root of, this is as simplified as it gets.

 
(return to problem 2a)

 


 

checkAnswer/Discussion to 3a

problem 3a
 

Even though 40 is not a perfect cube, it does have a factor that we can take the cube root of.

Check it out:
 

ad3a

*Rewrite 40 as (8)(5)

*Use the prod. rule of radicals to rewrite
*The cube root of 8 is 2
 
 

In this example, we are using the product rule of radicals in reverse to help us simplify the cube root of 40.  When you simplify a radical, you want to take out as much as possible.  The factor of 40 that we can take the cube root of is 8.  We can write 40 as (8)(5) and then use the product rule of radicals to separate the 2 numbers.  We can take the cube root of 8, which is 2, but we will have to leave the 5 under the cube root.

 
(return to problem 3a)

 


 

checkAnswer/Discussion to 3b

problem 3b
 

Even though ad3b    is not a perfect square, it does have a factor that we can take the square root of.

Check it out:
 

ad3b2

*Rewrite ad3b as ad3b4

*Use the prod. rule of radicals to rewrite
*The square root of ad3b3 is ad3b5
 
 

In this example, we are using the product rule of radicals in reverse to help us simplify the square root of ad3b.  When you simplify a radical, you want to take out as much as possible. 

The factor of ad3b that we can take the square root of is ad3b3 .  We can write ad3b as ad3b4  and then use the product rule of radicals to separate the two numbers.  We can take the square root of ad3b3which is ad3b5, but we will have to leave the rest of it under the square root.
 
 

(return to problem 3b)

 


 

checkAnswer/Discussion to 4a

problem 4a
 

ad4a1
*Use the  quotient rule of radicals to rewrite
 

*Simplify fraction
*Take the square root
 
 

Note that both radicals have an index number of 2, so we are able to put their quotient together under one radical keeping the 2 as its index number. Since the radicand is a perfect square, we are able to take the square root of the whole thing, which leaves us with nothing under the radical sign. 

 
(return to problem 4a)

 

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WTAMU > Virtual Math Lab >Intermediate Algebra >Tutorial 39: Simplifying Radical Expressions


Last revised on July 19, 2011 by Kim Seward.
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