Question

What is the $\sqrt{384}$ in simplest radical form?

Answer 1

Hint: In this question, we have to find the simplest radical form of an expression. Thus, we will use the least common multiple method to get the required solution. We start solving this problem, by first finding the LCM of the number 384. After that, we will make the pairs of two all the same terms. In the last, we will take a single number from the pairs and put it outside the square root sign, and the left non pair terms are put inside the square root, to get the required solution for the problem.

Complete step by step solution:
According to the problem, we have to find the simplest radical form of an expression.
Thus, we will use the least common multiple method to get the required solution.
The expression given to us is $\sqrt{384}$ in simplest radical form -------- (1)
So, we will first find the least common multiple of 384, that is
$\begin{align}
  & 2\left| \!{\underline {\,
 384 \,}} \right. \\
 & 2\left| \!{\underline {\,
 192 \,}} \right. \\
 & 2\left| \!{\underline {\,
 96 \,}} \right. \\
 & 2\left| \!{\underline {\,
 48 \,}} \right. \\
 & 2\left| \!{\underline {\,
 24 \,}} \right. \\
 & 2\left| \!{\underline {\,
 12 \,}} \right. \\
 & 2\left| \!{\underline {\,
 6 \,}} \right. \\
 & 3\left| \!{\underline {\,
 3 \,}} \right. \\
 & \text{ }\left| \!{\underline {\,
 1 \,}} \right. \\
\end{align}$
Thus, we get the least common multiple of 384 equals to
$\Rightarrow 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3$
Thus, now we will form the pairs in the above expression, we get
 $\Rightarrow \underline{2\times 2}\times \underline{2\times 2}\times \underline{2\times 2}\times 2\times 3$
Thus, we will now take the single terms from the pairs and put it outside the square root, we get
$\Rightarrow 2\times 2\times 2\sqrt{{}}$
Also, we will put the single terms inside the square root, we get
$\Rightarrow 2\times 2\times 2\sqrt{2\times 3}$
On further simplification, we get
$\Rightarrow 8\sqrt{6}$ which is the required solution.
Therefore, the simplest radical form of $\sqrt{384}$ is equal to $8\sqrt{6}$ .

Note: While solving this problem, do the step by step calculations properly to avoid confusion and mathematical error. Make the pairs of two terms and not three terms because we have to find the square root of 384 and not the cube root of 384.