We are given the equation:

\[
1343.501 = \frac{1}{2} \sqrt{\frac{k}{0.176}}
\]

### Step 1: Isolate the square root term.
Multiply both sides of the equation by 2 to eliminate the \(\frac{1}{2}\) on the right-hand side:

\[
2 \times 1343.501 = \sqrt{\frac{k}{0.176}}
\]

\[
2687.002 = \sqrt{\frac{k}{0.176}}
\]

### Step 2: Square both sides to eliminate the square root.
Square both sides of the equation to get rid of the square root:

\[
(2687.002)^2 = \frac{k}{0.176}
\]

\[
7211910.736004 = \frac{k}{0.176}
\]

### Step 3: Solve for \(k\).
Multiply both sides by 0.176 to isolate \(k\):

\[
k = 7211910.736004 \times 0.176
\]

\[
k = 1269550.2911367
\]

Thus, the value of \(k\) is approximately:

\[
k \approx 1269550.29
\]

---

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you solve other types of radical equations?
2. Can you derive a formula for \(k\) from this equation?
3. How does squaring both sides of an equation affect the solution?
4. How would you handle the equation if there was a negative square root?
5. What if there was a coefficient inside the square root?

**Tip:** Always check if you need to isolate terms before applying operations like squaring to avoid complications.

Learn how to solve the radical equation 1343.501 = 1/2 * sqrt(k / 0.176) with a detailed step-by-step solution. The problem involves isolating the square root, squaring both sides, and solving for k. Suitable for students in Grades 9-12.

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