Germany l A Nice Radical Problem l Math Olympiad

[@PrithwirajSen-nj6qq]

Rationalization of denominator (√108 +√81)^2/(108-81) =(108+81+2√(108*81) /27 =(108+81+2*9*2*3*√3) /27 =27(4+3+4√3)/27 =7+4√3 Sir it will take less time

[@ganeshdas3174]

(2 + √3) ^2 is the end result.

[@key_board_x]

= (√108 + √81)/(√108 - √81) → √108 = √(36 * 3) = √36 * √3 = 3√3 = (6√3 + √81)/(6√3 - √81) → √81 = 9 = (6√3 + 9)/(6√3 - 9) = [3.(2√3 + 3)]/[3.(2√3 - 3)] = (2√3 + 3)/(2√3 - 3) = (2√3 + 3).(2√3 + 3)/[(2√3 - 3).(2√3 +3)] = (2√3 + 3)²/[(2√3)² - (3)²] = (12 + 12√3 + 9)/[12 - 9] = (21 + 12√3)/3 = 7 + 4√3