Question

A farmer needs to fertilize a large rectangular field. He knows the width of the field is 50sqrt(3)/sqrt(2) yards and the length is 80sqrt(5)/sqrt(3) yards. What is the total area of the field that needs to be fertilized? (Recall that the area of a rectangle is the product of the width and the length.)
A.
2000sqrt(10)/3 square yards
B.
2000sqrt(10)/sqrt(3) square yards
C.
2000sqrt(10) square yards
D.
2000(sqrt6 + sqrt15) square yards

Answer 1

anyway I've added the missing information if you want to take a stab at it

Answer 2

well, alright, I'll take a shot if nobody else wants to

the sqrt(3) cancels out to get

50 * 80 sqrt(5) / sqrt(2)

we can mutliply both the numerator and denominator by sqrt(2) to eliminate the root in the denominator

50 * 80 * sqrt(5) * sqrt(2) / 2

should be clear after you simplify