[{(2)1/2 . (4)3/4 . (8)5/6 . (16)7/8 . (32)9/10}4]3/25 is
  • a)
    A fraction
  • b)
    an integer
  • c)
    1
  • d)
    none of these
Correct answer is option 'B'. Can you explain this answer?

CA Foundation Question

3 Answers
Abhishek Mehta answered Nov 16, 2018
x={[(125)2/3⋅(8)5/6⋅(16)7/8⋅(32)9/10]4}3/25
=[(53⋅2/3⋅23⋅5/6⋅24⋅7/8⋅25⋅9/10)4]3/25=[(52⋅25/2⋅27/2⋅29/2)4]3/25=[(52⋅25/2+7/2+9/2)4]3/25=
=[(52⋅221/2)4]3/25=[58⋅242]3/25=524/25⋅2126/25=524⋅2126−−−−−−−√25=32524⋅2−−−−−√25
x≈154,24190566187577033261129981792
so option B is correct

Chhavi Parakh answered Jul 24, 2020
[{2^1/2*2^3/2*2^5/2*2^7/2*2^9/2}*2^2]^3/25
=[2^1/2+3/2+5/2+7/2+9/2+4/2]^3/25
=[2^1+3+5+7+9+4/2]^3/25
=[2^29/2]^3/25 =2^29*3/2*25
=2^87/50 (option b) and integer

Shikha Singh answered Jul 28, 2020
An integer..

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