[rationalizing denominators][section 62]
         _
(1.)  3/
5                  here is the problem
        _   _  _                        _  _
=   (3/
5)(5/5)          multiply by 5/5
        _
=    (3
5)/5                    multiply, cancel
          _
(2.)   2/
3               here is the problem
        _    _  _                          _  _
=   (2/
3)/(3/3)           multiply by (3/3)
        _
=    (2
3)/3                  multiply, cancel
       _  _
(3.) 
8/3              here is the problem
      _ _    _
=   (
42)/(3)         factor the top
       _    _
=   (2
2)/(3)              take square root
        _  _    _  _                         _  _
=    (2
2/3)*(3/3)          multiply by (3/3)
         _
=     (2
6)/3               multiply and cancel
         _  _
(4.)   3
3/√2                  here is the problem
        _  _   _  _                             _  _
=    (3√3/√2)(√2/√2)              multiply by (√2/√2)
      _
=   3√6/2                   multiply
         _
(5.)   2√7
      ____
         _          
       5√3                    here is the problem

=
         _
(6.)   5√3
       ____                    here is the problem
         __
        √18
          _
=      5/√6                   reduce
           _   _  _                           _  _
=      (5/√6)(√6/√6)            multiply by (√6/√6)
        _
=     5√6/6             multiply
          _
(7.)   4/√a                 here is the problem
         _   _  _                          _  _
=    (4/√a)(√a/√a)           multiply by (√a/√a)
       _
=    4√a/a                     multiply
        _____
(8.)   √3/b3
                 here is the problem
       ____    ___                        ___
=    
3/b3 * b/b           multiply by b/b
      __
=   
3b/b2       multiply, take square root of b4
       ____ ___
(9.) 
b3d4/bd           here is the problem
       ____
=    
b2d3                   divide, cancel
         ____  __
(10.)  
24b3/6b          here is the problem
       ___
=    
4b2             divide, subtract exponents

=      2b               take square root