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# Hello Scott, Why is it important to simplify radical expressions

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.

Hi there,

Do you have any classmates' expressions yet?

-Scott

Customer: 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.

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.

sqrt(8) + sqrt(2)

Solution:

sqrt(4*2) + sqrt(2)

= 2sqrt(2) + sqrt(2)

= 3sqrt(2)

Thanks, XXXXX XXXXX post the classmates' ones :)

-Scott

Customer: 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

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

5√2 + 8√2

7√45 - 2√5

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

√5a+2√45a3

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

7√(5&3x) + 5√(5&3) x - âˆ›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 âˆ™ √15

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

5√2 + 8√2

7√45 - 2√5

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

√5a+2√45a3

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

7√(5&3x) + 5√(5&3) x - âˆ›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 âˆ™ √15

No problem!

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

Thanks,

Scott

Customer: 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

Here you go!

5√2 + 8√2
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)

√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 - âˆ›3x =

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