Irrational numbers

The governing concept is simplifying radicals by expressing each radicand as a perfect square multiplied by the same number. Since 75 = 25 × 3, √75 = 5√3. Since 147 = 49 × 3, √147 = 7√3. Thus y = 5√3 + 7√3 = 12√3. Dividing by √3 gives y/√3 = 12√3/√3 = 12. Therefore option B is correct. Option A or C could result from an incorrect addition of the coefficients, while option D may come from using an incorrect square factor in one of the radicals. The important point is that only like surds can be combined directly, so both terms must first be written as multiples of √3.