Question

The square root of three times a number is equal to two-fifths of that number.

Answer 1

Let the unknown number be denoted by \( x \). According to the problem, we have the equation:

\[
\sqrt{3}x = \frac{2}{5}x
\]

To solve for \( x \), we can start by isolating \( x \). First, we need to eliminate \( x \) from one side of the equation. We can do this by subtracting \( \frac{2}{5}x \) from both sides:

\[
\sqrt{3}x - \frac{2}{5}x = 0
\]

Next, we'll factor \( x \) out from the left side:

\[
x\left(\sqrt{3} - \frac{2}{5}\right) = 0
\]

This equation gives us two potential solutions:

1. \( x = 0 \)
2. \( \sqrt{3} - \frac{2}{5} = 0 \)

Now, we can solve for the second case:

\[
\sqrt{3} = \frac{2}{5}
\]

However, since \( \sqrt{3} \) is approximately \( 1.732 \) and \( \frac{2}{5} = 0.4 \), we see that \( \sqrt{3} \neq \frac{2}{5} \). Thus, the only solution we have is:

\[
x = 0
\]

Therefore, the solution to the equation is:

\[
\boxed{0}
\]