Final answer:
The new value of Quantity B will be the original value divided by the square root of 6, as Quantity B is proportional to the square root of Quantity A.
Step-by-step explanation:
If there is a square root relationship between Quantity A and Quantity B, it implies that B is proportional to the square root of A, which we can write as B ∝ √A (where √ denotes square root).
When Quantity A is divided by 6, we can denote the new quantity as A'. Thus, A' = A/6. To find the new value of Quantity B, which we'll call B', we take the square root of A' and compare it to the original B.
B = k·√A (where k is the constant of proportionality)
B' = k·√A' = k·√(A/6)
Because √(A/6) = √A/√6, we can say that B' = B/√6.
To put it simply, the new value of Quantity B is the old value divided by the square root of 6.