[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