Question

When a > 0, which expression is equivalent to √150a³ in simplest form?A. 6a√5aB. 5a³√6C. 5a√6aD. a³√150

Answer 1

C. 5a√6a

Step-by-step explanation:

Given the expression:

`\sqrt[]{150a^3}`

First, write the term as a product of the number and algebraic expression:

`=\sqrt[]{150* a^3}`

Next, express the number 150 as a product of a perfect square and another number:

`\begin{gathered} =\sqrt[]{25*6* a^2* a} \\ =\sqrt[]{25* a^2*6* a} \\ =\sqrt[]{25* a^2}*\sqrt[]{6* a} \\ =5* a*\sqrt[]{6a} \\ =5a\sqrt[]{6a} \end{gathered}`

The correct choice is C,