 √𝑥 is a rational number between √125 and √150. Find a value for 𝑥

To solve the problem, we need to find a value of \( x \) such that \( \sqrt{x} \) is a rational number between \( \sqrt{125} \) and \( \sqrt{150} \).

### Step 1: Calculate the approximate values of \( \sqrt{125} \) and \( \sqrt{150} \).
- \( \sqrt{125} \approx 11.18 \)
- \( \sqrt{150} \approx 12.25 \)

### Step 2: Identify the rational numbers between these two values.
We need to find a perfect square number \( n^2 \) such that:
\[
11.18 < n < 12.25
\]
The integer value of \( n \) that satisfies this condition is \( n = 12 \).

### Step 3: Calculate \( x \).
Since \( \sqrt{x} = n \), we set \( n = 12 \), so:
\[
x = n^2 = 12^2 = 144
\]

### Conclusion
The value of \( x \) that satisfies the condition is \( \boxed{144} \).

Would you like more details or have any questions?

Here are 5 related questions:
1. What are rational numbers, and how are they defined?
2. How do you calculate the square root of a non-perfect square?
3. What are perfect squares, and how do they relate to rational numbers?
4. How can we approximate square roots of non-perfect squares?
5. Can you find another example where \( \sqrt{x} \) is a rational number between two given square roots?

**Tip:** When solving problems involving square roots, identifying perfect squares can be a useful strategy to find rational solutions.

√𝑥 is a rational number between √125 and √150. Find a value for 𝑥.

Solve the problem where √𝑥 is a rational number between √125 and √150. Learn about square roots, rational numbers, and how perfect squares help in finding the value of 𝑥. This detailed step-by-step guide is suitable for students in Grades 9-10.

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