SOLUTION: for each indicated sum and/or difference,simplify the radicals and combine when possible 5x square root 72 + square 8x^2 a square root 125y-b square root 45y square root

for each indicated sum and/or difference,simplify 
the radicals and combine when possible.

That's too many to post.  Here are three of them.
You do the rest. They're similar:

   __    ___ 
5xÖ72 + Ö8x²

Break 72 into prime factors

72 = 8·9 = 2·4·3·3 = 2·2·2·3·3

Break 8x² into prime factors

8x² = 2·4·x·x = 2·2·2·x·x

Substitute under radicals:
   _________    _________
5xÖ2·2·2·3·3 + Ö2·2·2·x·x

Group like factors into pairs:
   _____________    _____________
5xÖ(2·2)·2·(3·3) + Ö(2·2)·2·(x·x)

Write each pair as a square:
   _______    _______
5xÖ2²·2·3² + Ö2²·2·x²

Take the squares out in front of the radicals
as non-square factors:
       _       _
5x·2·3Ö2 + 2·xÖ2
    _      _
30xÖ2 + 2xÖ2 
             _
Factor out xÖ2
  _
xÖ2(30 + 2)
  _
xÖ2(32)
    _
32xÖ2

===========================================
      __         __    __         __
(1/3)Ö45 - (1/2)Ö12 + Ö20 + (2/3)Ö27

Break 45 into prime factors

45 = 9·5 = 3·3·5

Break 12 into prime factors

12 = 4·3 = 2·2·3

Break 20 into prime factors

20 = 4·5 = 2·2·5

Break 27 into prime factors

27 = 9·3 = 3·3·3

Substitute under radicals

      _____         _____    _____         _____
(1/3)Ö3·3·5 - (1/2)Ö2·2·3 + Ö2·2·5 + (2/3)Ö3·3·3

Group like factors into pairs:

      _______         _______    _______         _______
(1/3)Ö(3·3)·5 - (1/2)Ö(2·2)·3 + Ö(2·2)·5 + (2/3)Ö(3·3)·3

Write each pair as a square:
      ____         ____    ____         ____
(1/3)Ö3²·5 - (1/2)Ö2²·3 + Ö2²·5 + (2/3)Ö3²·3

Take the squares out in front of the radicals
as non-square factors:

        _           _     _           _
(1/3)·3Ö5 - (1/2)·2Ö3 + 2Ö5 + (2/3)·3Ö3
 _    _     _     _ 
Ö5 - Ö3 + 2Ö5 + 2Ö3

Group like radical terms together
 _     _    _     _  
Ö5 + 2Ö5 - Ö3 + 2Ö3
        _                             _
Factor Ö5 out of first two terms and Ö3 out of 
last two terms:
 _           _
Ö5(1 + 2) + Ö3(-1 + 2)
 _       _
Ö5(3) + Ö3(1)
  _    _ 
3Ö5 + Ö3

==============================================
  ______     _______
aÖ5000b³ + 2Ö125a³b²

Break 5000b³ into prime factors:

5000b³ = 2·2500·b·b·b = 2·2·1250·b·b·b = 2·2·2·625·b·b·b =
          = 2·2·2·5·125·b·b = 2·2·2·5·5·25·b·b·b = 
             = 2·2·2·5·5·5·5·b·b·b

Break 125a³b² into prime factors

125a³b² = 5·25·a·a·a·b·b = 5·5·5·a·a·a·b·b

Substitute under radicals:
  ___________________      _______________
aÖ2·2·2·5·5·5·5·b·b·b  + 2Ö5·5·5·a·a·a·b·b

Group like factor into pairs:
  ___________________________      _____________________
aÖ(2·2)·2·(5·5)·(5·5)·(b·b)·b  + 2Ö(5·5)·5·(a·a)·a·(b·b)

Write each pair as a square:
  _______________      ____________
aÖ2²·2·5²·5²·b²·b  + 2Ö5²·5·a²·a·b²

Take the squares out in front of the radicals
as non-square factors:

          ___            ___
a·2·5·5·bÖ2·b  + 2·5·a·bÖ5·a
     __        __
50abÖ2b + 10abÖ5a

Factor out 10ab
       __    __ 
10ab(5Ö2b + Ö5a)

Edwin