Let's denote the two numbers as x and y. We know that the square root of two numbers is 5 square root 3, so we can write:
sqrt(x) + sqrt(y) = 5sqrt(3)
We also know that one of the numbers is 3, so we can substitute x = 3 into the equation:
sqrt(3) + sqrt(y) = 5sqrt(3)
Now we can solve for y by isolating the square root term:
sqrt(y) = 5sqrt(3) - sqrt(3)
sqrt(y) = 4sqrt(3)
Squaring both sides of the equation gives:
y = (4sqrt(3))^2
y = 48
Therefore, the other number is 48.