Question

x
6
=16
Solve for a positive value of xx, expressing your answer with a radical symbol.
xx =

Answer 1

To solve for \( x \) in the equation

\[
\frac{x}{6} = 16,
\]

start by isolating \( x \). Multiply both sides of the equation by 6:

\[
x = 16 \times 6.
\]

Calculating the right side gives:

\[
x = 96.
\]

Now, to express \( x \) with a radical symbol, we can rewrite 96 in terms of radicals. Notably, we recognize:

\[
96 = 16 \times 6 = 16 \times (2 \sqrt{6}) = 4^2 \times (2 \sqrt{6}).
\]

But to clearly express 96 using a radical, it can be factored as:

\[
96 = 4 \sqrt{144}.
\]

Thus, we can write it as:

\[
x = 4\sqrt{24}.
\]

However, the simplest radical form for \( x \):

\[
x = 8\sqrt{6}.
\]

So, the positive value of \( x \) expressed with a radical symbol is

\[
\boxed{8\sqrt{6}}.
\]

Note: Here, \( x = 96 \) is still the simplest numerical value; without a requirement for a radical form specifically written in terms of smaller components, \( x = 96 \) is often preferred as the immediate numerical solution.