Brazil | You Should Know this Trick | A nice Math Olympiad Algebra | Radical Simplification

[@ritwikgupta3655]

Nice solution, very well handled.

[@superacademy247]

Sure is

[@walterwen2975]

A nice Math Olympiad Algebra, Simplify: {(³√100 - 1)/[3(³√10) + 3]}⁵ = ? ³√100 - 1 = (³√10)² - 1 = (³√10 - 1)(³√10 + 1), 3(³√10) + 3 = 3(³√10 + 1) (³√100 - 1)/[3(³√10) + 3] = [(³√10 - 1)(³√10 + 1)]/[3(³√10 + 1)] = (³√10 - 1)/3 {(³√100 - 1)/[3(³√10) + 3]}⁵ = [(³√10 - 1)/3]⁵ = [(³√10 - 1)⁵]/3⁵ (³√10 - 1)⁵ = (³√10)⁵ - 5(³√10)⁴ + 10(³√10)³ - 10(³√10)² + 5(³√10) - 1 = 10(³√10)² - 50(³√10) + 10(10) - 10(³√10)² + 5(³√10) - 1 = 99 - 45(³√10) [(³√10 - 1)/3]⁵ = [99 - 45(³√10)]/3⁵ = {3²[11 - 5(³√10)]}/3⁵ = [11 - 5(³√10)]/27 Answer check: (³√100 - 1)/[3(³√10) + 3] = (³√10 - 1)/3 [(³√10 - 1)/3]⁵ = (1.154/3)⁵ = 0.385⁵ = 0.0084 [11 - 5(³√10)]/27 = 0.2278/27 = 0.0084; Confirmed Math calculation was achieved on a smartphone with a standard calculator app Final answer: Simplified form; {(³√100 - 1)/[3(³√10) + 3]}⁵ = [11 - 5(³√10)]/27