CA Foundation Exam > CA Foundation Questions > [{(2)1/2. (4)3/4. (8)5/6. (16)7/8. (32)9/10}4...
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[{(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?
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[{(2)1/2. (4)3/4. (8)5/6. (16)7/8. (32)9/10}4]3/25isa)A fractionb)An i...
Given expression: [{(2)1/2. (4)3/4. (8)5/6. (16)7/8. (32)9/10}4]3/25
Simplifying innermost brackets:
(2)1/2 = √2
(4)3/4 = (2^2)3/4 = 2^3/2 = 8
(8)5/6 = (2^3)5/6 = 2^5/2 = 32
(16)7/8 = (2^4)7/8 = 2^7/2 = 128
(32)9/10 = (2^5)9/10 = 2^9/2 = 512
The expression now becomes: [{√2. 8. 32. 128. 512}4]3/25
Simplifying further:
{√2. 8. 32. 128. 512}4 = (2^(-1/2) * 2^3 * 2^5 * 2^7 * 2^9)4 = 2^37
[{√2. 8. 32. 128. 512}4]3/25 = (2^37)3/25 = 2^(37/25)
Since 37/25 is not an integer, the answer cannot be an integer or a fraction in reduced form. Therefore, the answer is an irrational number and option (d) None of these is the correct answer.
Simplifying innermost brackets:
(2)1/2 = √2
(4)3/4 = (2^2)3/4 = 2^3/2 = 8
(8)5/6 = (2^3)5/6 = 2^5/2 = 32
(16)7/8 = (2^4)7/8 = 2^7/2 = 128
(32)9/10 = (2^5)9/10 = 2^9/2 = 512
The expression now becomes: [{√2. 8. 32. 128. 512}4]3/25
Simplifying further:
{√2. 8. 32. 128. 512}4 = (2^(-1/2) * 2^3 * 2^5 * 2^7 * 2^9)4 = 2^37
[{√2. 8. 32. 128. 512}4]3/25 = (2^37)3/25 = 2^(37/25)
Since 37/25 is not an integer, the answer cannot be an integer or a fraction in reduced form. Therefore, the answer is an irrational number and option (d) None of these is the correct answer.
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