Question

Express $8\sqrt{18}$ in the form $a\sqrt b$, where $a$ and $b$ are integers and $b$ is as small as possible.

Answer 1

8 √18 = 8 √(9 × 2)

= 8 √(3² × 2)

= 8 √(3²) √2

= (8 × 3) √2

= 24 √2

Answer 2

24 √2

Step-by-step explanation:

The largest square factor under the radical is $9$. This gives us the factorization $\sqrt{18} = \sqrt 9 \cdot \sqrt 2$. Thus

\begin{align*}

8\sqrt{18} &= 8(\sqrt 9\cdot \sqrt 2) \\

&= 8\cdot 3\sqrt 2 \\

&= \boxed{24\sqrt 2}.

\end{align*}