Given √224r = 13r the value of radix r is, ISRO 2018

Convert the given numbers from radix r to base 10. The number 224_r equals 2r^2 + 2r + 4, and 13_r equals r + 3. The equation becomes sqrt(2r^2 + 2r + 4) = r + 3. Squaring both sides gives 2r^2 + 2r + 4 = r^2 + 6r + 9. Rearranging terms results in the quadratic equation r^2 - 4r - 5 = 0. Factoring yields (r - 5)(r + 1) = 0, so r = 5 or r = -1. Since the radix must be greater than the largest digit (4), r = 5 is the valid solution.