Question

The product `root(3)(2) * root(4)(2) * root(12)(32)` equals to ______.

पर्याय

• `sqrt(2)`

• 2

• `root(12)(2)`

• `root(12)(32)`

Answer 1

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