The equation you're working with is:

\[
3 = \frac{\lambda 1}{L^{0.5}}
\]

To solve for \( \lambda \), let's go step by step.

### Step 1: Isolate \( \lambda \)
Multiply both sides of the equation by \( L^{0.5} \) to get rid of the denominator on the right-hand side:

\[
3 \times L^{0.5} = \lambda 1
\]

### Step 2: Simplify the equation
Since \( \lambda 1 \) is just \( \lambda \), we can rewrite this as:

\[
\lambda = 3 \times L^{0.5}
\]

Thus, the solution is:

\[
\lambda = 3 \sqrt{L}
\]

Would you like more details or further clarification?

### Related Questions:
1. How does squaring both sides work when isolating a variable?
2. What are the steps to solve equations involving square roots?
3. Can this equation be rearranged if other variables are known?
4. How does the constant 3 affect the proportionality between \( \lambda \) and \( L \)?
5. Can \( L \) be a negative number in this equation?

### Tip:
Always ensure that the exponent rules (such as \( L^{0.5} = \sqrt{L} \)) are correctly applied when solving algebraic equations.

Learn how to solve for lambda in the equation 3 = λ / L^0.5 with a step-by-step guide. This problem covers algebraic concepts such as isolating variables and solving equations involving square roots. Suitable for students in Grades 9-11.

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