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Hello Scott, Why is it important to simplify radical expressions

Hello Scott, Why is it important...
Hello Scott,

Why is it important to simplify radical expressions before adding or subtracting? How is adding radical expressions similar to adding polynomial expressions? How is it different? Provide a radical expression for your classmates to simplify. Consider participating in the discussion by simplifying your classmates' expressions. Detail what would have happened if the expression was not simplified first.
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2/7/2012
Scott
Scott, MIT Graduate
Category: Pre-Calculus
Satisfied Customers: 17,710
Experience: Over 13,000 accepts & 100% feedback in the old math category
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Hi there,

 

Do you have any classmates' expressions yet?

 

-Scott

 

 

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Customer reply replied 5 years ago
Yes, like 10!

Ok, you can post them here, and I'll respond to each of them :)

 

Why is it important to simplify radical expressions before adding or subtracting?

You have to simplify radical expressions before you add or subtract them because you can only combine them if they are like terms -- meaning if the value inside the root is the same, and the index of the root is the same.

 

How is adding radical expressions similar to adding polynomial expressions? How is it different?

This is similar to adding polynomials, because for those also, you can only add like terms. The main difference is the definition of like terms. For radicals, it means the same value inside the root and same index. For polynomials, it means that the variables and the powers on them are the same.

 

Provide a radical expression for your classmates to simplify.

sqrt(8) + sqrt(2)

 

Solution:

sqrt(4*2) + sqrt(2)

= 2sqrt(2) + sqrt(2)

= 3sqrt(2)

 

Thanks, XXXXX XXXXX post the classmates' ones :)

-Scott

Scott
Scott, MIT Graduate
Category: Pre-Calculus
Satisfied Customers: 17,710
Experience: Over 13,000 accepts & 100% feedback in the old math category
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Customer reply replied 5 years ago
Great, thank you so much. Can i post them later tonight, I just got ann emergency and I have to leave!

No problem! I hope everything is okay!

-Scott

Scott
Scott, MIT Graduate
Category: Pre-Calculus
Satisfied Customers: 17,710
Experience: Over 13,000 accepts & 100% feedback in the old math category
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Customer reply replied 5 years ago
Good morning Scott,
Here are my class mates post. I really appreciate this.

1.)Add or Subtract. Simplify by collecting like radical terms if possible.

5√2 + 8√2

7√45 - 2√5

2.)The square root of 3p plus the square root of 7q.

3.)Add and simplify

√5a+2√45a3

4.)Here is a radical expression for the class to solve:

7√(5&3x) + 5√(5&3) x - ∛3x =

5.)Problems for my classmates...
Simplify:
√45
√21/9

6.)Simplify
√36a2b2

7.)problem for the class
√5 * 3√2

8.)2√8+z + 4√4+z

5√6+x + 10√2+x3

9.)Examples for the class:
-√81
√36/16

10.)Example for the class
√ 12 ∙ √15











Customer reply replied 5 years ago
** For Scott ONLY **
Good morning Scott,
Here are my class mates post. I really appreciate this.

1.)Add or Subtract. Simplify by collecting like radical terms if possible.

5√2 + 8√2

7√45 - 2√5

2.)The square root of 3p plus the square root of 7q.

3.)Add and simplify

√5a+2√45a3

4.)Here is a radical expression for the class to solve:

7√(5&3x) + 5√(5&3) x - ∛3x =

5.)Problems for my classmates...
Simplify:
√45
√21/9

6.)Simplify
√36a2b2

7.)problem for the class
√5 * 3√2

8.)2√8+z + 4√4+z

5√6+x + 10√2+x3

9.)Examples for the class:
-√81
√36/16

10.)Example for the class
√ 12 ∙ √15











No problem!


Can you confirm #4 and #10, which have funny symbols?


Thanks,

Scott

Ask Your Own Pre-Calculus Question
Customer reply replied 5 years ago
Hmm, your right!! Don't worry about 4 and 10. I'll post a couple of new ones as soon as I see more. Thank you. I have to run to school now so I can accept your answer in about 4-5 hours. Thank you :)

Ok, I'll have these for you in a bit :)

-Scott

Ask Your Own Pre-Calculus Question

Here you go!


1.)Add or Subtract. Simplify by collecting like radical terms if possible.

5√2 + 8√2
The value in the radical is the same, so add:
13 sqrt 2

 

7√45 - 2√5
Simplify:
7sqrt(9*5) - 2sqrt(5)
21sqrt(5) - 2sqrt(5)
19 sqrt 5

 

2.)The square root of 3p plus the square root of 7q.
These are unlike roots, so you cannot do anything:
sqrt(3p) + sqrt(7q)

 

3.)Add and simplify

√5a+2√45a3
Factor the second term:
sqrt(5a) + 2sqrt(9a^2 * 5a)
= sqrt(5a) + 6a sqrt(5a)
Factor:
(1+6a) sqrt(5a)

 


4.)Here is a radical expression for the class to solve:

7√(5&3x) + 5√(5&3) x - ∛3x =
Please retype

 

5.)Problems for my classmates...
Simplify:
√45
= sqrt(9*5)
= 3 sqrt 5


√21/9
sqrt(21/9)
= sqrt(21)/3

 

6.)Simplify
√36a2b2
= sqrt((6ab)^2)
= 6ab

 

7.)problem for the class
√5 * 3√2
Multiply on the inside of the root:
3 sqrt 10


8.)2√8+z + 4√4+z
Assuming the 8+z and 4+z are inside the roots, they are not like roots, so nothing can be done.

 

5√6+x + 10√2+x3
Assuming the 6+x and 2+x^3 are inside the roots, they are not like roots, so nothing can be done.


9.)Examples for the class:
-√81
= -sqrt(9*9)
= -9


√36/16
=sqrt(36)/sqrt(16)
= 6/4
= 3/2

 

10.)Example for the class
√ 12 âˆTM √15
Please retype


Let me know if you have any questions,
Scott

Scott
Scott, MIT Graduate
Category: Pre-Calculus
Satisfied Customers: 17,710
Experience: Over 13,000 accepts & 100% feedback in the old math category
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Scott
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Satisfied Customers: 17,710
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