[tex] Bentuk sederhana dari ( \sqrt{52+ 6 \sqrt{43} } ) ^{3} - ( \sqrt{52 - 6 \sqrt{43} } ) ^{3} adalah... [/tex]

Bab Bilangan Irrasional
Matematika SMP Kelas IX

(√(52 + 6√43))³ - (√(52 - 6√43))³
= (√(52 + 2 . 3√43))³ - (√(52 - 2 . 3√43))³
= (√(52 + 2 √(43 . 3²)))³ - (√(52 - 2 √(43 . 3²)))³
= (√(43 + 9 + 2 √(43 . 9)))³ - (√(49 + 9 - 2 √(43 . 9)))³
= (√43 + √9)³ - (√43 - √9)³
= (√(43) + 3)³ - (√(43) - 3)³
= (√43³ + 3 . (√43)² . 3 + 3 . (√43) . 3² + 3³) - (√43³ - 3 . (√43)² . 3 + 3 . (√43) . 3² - 3³)
= 2 . 9 . 43 + 2 . 27
= 774 + 54
= 828