√3(√30 + √8) can be simplified into the follwing format: x√10 + y√6 where are x and y are integers. Find the value of x and y.
Begin by expansion (√a x √b = √ab): √3 x √30 = √90 and √3 x √8 = √24. Therfore we have: √90 + √24. Simplify roots (√a^2√b). The question tells us we need x√10 so therefore √90 = √9√10 (9x10 = 90) and we need y√6 so therefore √24 = √4√6 (4x6 = 24). Simplify square roots further: √9 = 3 or -3 and √4 = 2 or -2. The questions aks for x and y to be integers (positive whole numbers) so the final answer is:3√10 + 2√6 therefore x = 3 and y = 2
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