https://file.aiquickdraw.com/mathbot/file/1727373160562q2hekn1l.jpg

Let's break down and solve the numbers in the image:

1. **\( 1.5 \times 10^2 \)**:
   - This is scientific notation. 
   - \( 1.5 \times 10^2 = 1.5 \times 100 = 150 \).

2. **\( \sqrt{125} \)**:
   - The square root of 125 is approximately \( \sqrt{125} \approx 11.18 \).

3. **\( |-30| \)**:
   - The absolute value of \(-30\) is 30.
   - \( |-30| = 30 \).

### Now, let's arrange the numbers in ascending order (least to greatest):

- \( \sqrt{125} \approx 11.18 \)
- \( |-30| = 30 \)
- \( 1.5 \times 10^2 = 150 \)

Thus, the correct order is:

\[ \sqrt{125} < |-30| < 1.5 \times 10^2 \]
  
Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you calculate the square root of a non-perfect square?
2. What are the rules for working with absolute values in equations?
3. How do you convert scientific notation to standard form?
4. Can you think of examples where absolute value is used in real-life applications?
5. What are the properties of square roots when comparing numbers?

**Tip:** When comparing numbers in different forms (like scientific notation, square roots, and absolute values), always convert them to their decimal equivalents first!

Arrange the following three numbers in order from least to greatest: 1.5 × 10^2, √125, |-30|.

Learn how to arrange numbers like 1.5 × 10^2, √125, and |-30| in order from least to greatest. This math problem explores key concepts such as scientific notation, square roots, and absolute values, perfect for students in Grades 6-8.

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