1) To simplify 1/2√200 - 7√2/49 - √72:
First, simplify √200 = 10√21/2 * 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√31/5 * 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
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