(9 + √80)1.5 is equal to
Solution
Correct Answer: Option D
(9 + √80)1.5
= (9 + 4√5)1.5
= (4+5+ 2 × 2 × √5)3/2
= (22+(√5)2+2×2×√5)3/2
[Using the formula: (a + b)2 = a2 + b2 + 2ab and (a+b)3=(a3+b3+3a2b+3ab2)]
= [(2+√5)2]3/2
= (2+√5)3
= 8 + 5√5 + 12√5 + 30
= 38+ 17√5
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