Question

Question 18
The product $\sqrt[3]{32}.\sqrt[4]{42}.\sqrt[12]{1232}$ equals to
Thinking process
Take the LCM of indices of three irrational numbers. Then, convert all individually in the from whose index will be equal to LCM.

A) $\sqrt{2}$
B) $2$
C) $\sqrt[12]{122}$
D) $\sqrt[12]{1232}$

Answer 1

The answer is B.
LCM of 3,4 and 12 = 12.
$\sqrt[3]{32}=\sqrt[12]{122^4}[\because \sqrt[m]{ma}=\sqrt[mn]{mn{a}^n}]\sqrt[4]{42}=\sqrt[12]{122^3}$
and $\sqrt[12]{1232}=\sqrt[12]{122^5}$
$\therefore$ Product of $\sqrt[3]{32}.\sqrt[4]{42}.\sqrt[12]{1232}=\sqrt[12]{122^4}.\sqrt[12]{122^3}.\sqrt[12]{122^5}=\sqrt[12]{122^4{.2}^3{.2}^5}$
$=\sqrt[12]{122^{12}}=2^{12\times \frac{1}{12}}=2[\because \sqrt[m]{m{a}^n}=a^{n/m}]$