_    _
(1.)  √2 * √7             here is the problem
__
=    √14                 multiply
_    _
(2.)  √3 * √6           here is the problem
__
=    √18              multiply
_ _
=   √9√2             factor like this
_
=   3√2          take square root of the 9
_    __
(3.)  √5 * √10         here is the problem
__
=     √50              multiply
__    _
=      √25 * √2            factor like this
_
=      5√2         take square root of the 25
_    _
(4.)  √9 * √4        here is the problem

=    3 * 2            take square roots

=    6               multiply
_    _
(5.)  2√3 * √2         here is the problem
_
=     2√6               multiply
__     _
(6.)  -7√12 * 4√3          here is the problem
__
=    -28√36              multiply

=   -28(6)            take square root of the 36

=    -168                multiply
_      _
(7.)  -8√6 * -3√7       here is the problem
__
=     24√42             multiply
___     ____
(8.)  √6m4 *  √3mn2        here is the problem
______
=    √18m5n2                     here is the problem
_____   ___
=   √9m4n2 * √2m         factor like this
__
=    3m2n√2m          take square root
_     __
(9.)   \3/4 * \3/2         here is the problem
_
=    \3/8                     multiply

=    2                       take the cube root of 8
__      __
(10.)  -3a√ab * 2a√ab         here is the problem

=    -6a2(ab)              multiply

=  -6a3b                     multiply