Question

Which of the following is equivalent to sqrt (54a^3)/sqrt (2a) ?

Answer 1

The given expression is

`(√(54a^3))/(√(2a))`

Apply radical rule:

`\begin{gathered} (√(a))/(√(b))=\sqrt{(a)/(b)},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0 \\ (√(54a^3))/(√(2a))=\sqrt{(54a^3)/(2a)} \end{gathered}`

Cancel the common factor (2a), we will have

`=√(27a^2)`

Apply radical rule:

`\begin{gathered} √(ab)=√(a)√(b),\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0 \\ √(27a^2)=√(27)√(a^2) \\ √(a^2)=a,\:\quad \mathrm{\:assuming\:}a\ge 0 \\ =√(27)a \end{gathered}`

Then

`√(27)a=3√(3)a=3a√(3)`

Hence, the answer is

`3a√(3)\text{ \lparen Option 2\rparen}`