1) To simplify 1/2√200 - 7√2/49 - √72:

First, simplify √200 = 10√2
1/2 * 10√2 = 5√2

Second, simplify √72 = 6√2

Putting it all together:
5√2 - 7√2/49 - 6√2
= -2√2/49 - 6√2
= -2√2/49 - 294√2
= (-2/49 - 6)√2
= (-104/49)√2

2) To simplify 1/5√300 - 4√3/16 - √75:

First, simplify √300 = 10√3
1/5 * 10√3 = 2√3

Second, simplify √75 = 5√3

Putting it all together:
2√3 - 4√3/16 - 5√3
= -4√3/16 - 5√3
= -4√3/16 - 80√3
= (-4/16 - 80)√3
= (-84/16)√3
= (-21/4)√3