x

Question

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

$$\boxed{{\displaystyle 8\sqrt{6}}}.$$

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.