simplify:

sqrt ((7)/(100))

my work:

7 = 1sqrt (7)
100= 10 sqrt (1)

(1)/(10) sqrt (7)

my answer:

(sqrt (7))/(10)

Your answer is right but your statements:

7 = 1sqrt (7)
100= 10 sqrt (1)

make no sense.
how can sqrt(7)=7 ? you are saying 2.6457..=7

and 10sqrt(1) = 100 ---> 10 x 1 = 100 ??

I would write:

sqrt(7/100)
=sqrt(7) / sqrt(100)
= sqrt(7) / 10