Question

rationalize the denominator 3+2 root 5 / 3-2 root 5​

Answer 1

Answer:

(29 + 12√5)/11

Explanation:

(3+2√5)/(3-2√5)

[multiply both numerator and denominator by (3+2√5) to rationalise the denominator]

=> ( (3+2√5) × (3+2√5) ) / ( (3-2√5) × (3+2√5) )

note : (a+b) × (a-b) = a² - b²

=> ( (3+2√5)² ) / ( (3² - (2√5)²)

note : (a+b)² = a² + b² +2ab

=> ( 9+20+ 12√5 ) / ( 9-20 )

=> ( 29+12√5 ) / ( 11 )