algebra? are you math smart?

Question

the number of centimeters, d, that a spring is compressed from its natural uncompressed position is given by d=sq.rt2w/k,where k is the number of joules of work done to move the spring and k is the spring constant. solve this equation for w. use the result to determine the work needed to move a spring 4 centimeters if it has a spring constant of 0.2

Answer 1

There is a minor typo in the question because it says
"k is the number of joules of work", but it really
should reference "w". In any case, given:

d=sqrt(2*w/k)

Solving for w gives:

Square both sides:
d^2 = 2*w/k

Multiply both sides by "k" and "1/2":
k * d^2 = 2*w
1/2 * k * d^2 = w

Note that this agrees with the reference:
w = 1/2 * k * d^2


Given the specific case where k=0.2 and d=4cm:

w = 1/2 * 0.2 * (4)^2
w = 0.1 * 16
w = 1.6 joules

Answer 2

Your notation is unclear.

You'd do better to re-ask the question.