If y varies directly as the square root of x and y = 3 when x = 16. Calculate y when x = 64

Answer Details

If y varies directly as the square root of x, this means that the ratio between y and the square root of x remains constant. We can write this as: y/sqrt(x) = k where k is the constant of proportionality. We are given that y = 3 when x = 16. Using this information and the equation above, we can solve for k: 3/sqrt(16) = k 3/4 = k Now that we know k, we can use the same equation to find y when x = 64: y/sqrt(64) = 3/4 y/8 = 3/4 y = (3/4) * 8 y = 6 Therefore, when x = 64, y = 6. The answer is option B.