Question

If a and b are positive integers and $(a{b}^{3/2}{)}^2=108$, what is the value of $ab$?

• A. $4$
• B. $5$
• C. $6$
• D. $7$

Answer 1

The correct option is C $6$

Given, $(a{b}^{\frac{3}{2}}{)}^2=108$

$\Rightarrow \left(a^2{b}^3\right)=108$

As $108=2\times 2\times 3\times 3\times 3$

$\Rightarrow a=2,b=3$

$\Rightarrow ab=2\times 3=6$