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Question
The product `root(3)(2) * root(4)(2) * root(12)(32)` equals to ______.
Options
`sqrt(2)`
2
`root(12)(2)`
`root(12)(32)`
Solution
The product `root(3)(2) * root(4)(2) * root(12)(32)` equals to 2.
Explanation:
LCM of 3, 4 and 12 = 12
`root(3)(2) = root(12)(2^4)` ...`[∵ root(m)(a) = root(mn)(a^n)]`
`root(4)(2) = root(12)(2^3)`
And `root(12)(32) = root(12)(2^5)`
∴ Product of `root(3)(2) * root(4)(2) * root(12)(32) = root(12)(2^4) * root(12)(2^3) * root(12)(2^5)`
= `root(12)(2^4 * 2^3 * 2^5)`
= `12sqrt(2^(4 + 3 + 5))`
= `root(12)(2^12)` ...`[∵ root(m)(a^n) = a^(n/m)]`
= `2^(12 xx 1/12)`
= 2
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