https://file.aiquickdraw.com/mathbot/file/17292727039583z2b846k.jpg

Let's solve the problem step-by-step.

The task is to **order the numbers** from least to greatest and determine which number goes into the **yellow box**. The numbers given are:

\[
-\sqrt{2}, \quad \sqrt{3}, \quad 1.5, \quad -1.6, \quad -\sqrt{3}
\]

### Step 1: Approximate the square roots.
- \( \sqrt{2} \approx 1.414 \)
- \( \sqrt{3} \approx 1.732 \)

Thus:
- \( -\sqrt{2} \approx -1.414 \)
- \( \sqrt{3} \approx 1.732 \)
- \( -\sqrt{3} \approx -1.732 \)

### Step 2: Rewrite the numbers using their approximate values.
- \( -\sqrt{2} \approx -1.414 \)
- \( \sqrt{3} \approx 1.732 \)
- \( 1.5 \) stays as it is.
- \( -1.6 \) stays as it is.
- \( -\sqrt{3} \approx -1.732 \)

### Step 3: Order the numbers from least to greatest.
From least to greatest:
\[
-1.732 \, (\text{-}\sqrt{3}), \quad -1.6, \quad -1.414 \, (\text{-}\sqrt{2}), \quad 1.5, \quad 1.732 \, (\sqrt{3})
\]

### Step 4: Assign the numbers to the colored boxes.
- **Blue**: \( -\sqrt{3} \approx -1.732 \) (Least)
- **Red**: \( -1.6 \)
- **Yellow**: \( -\sqrt{2} \approx -1.414 \) (**Answer for the yellow box**)
- **Green**: \( 1.5 \)
- **Orange**: \( \sqrt{3} \approx 1.732 \) (Greatest)

### Final Answer:
The number that goes in the **yellow box** is:

\[
-\sqrt{2}
\]

---

Do you want further details or have any other questions?  
Here are 5 related questions to deepen your understanding:

1. How do you find exact square roots for non-perfect squares like \( \sqrt{2} \)?
2. What are the properties of irrational numbers like \( \sqrt{2} \) and \( \sqrt{3} \)?
3. How do negative numbers compare with positive ones in terms of size?
4. What are other real-life applications of ordering numbers?
5. How can you visualize irrational numbers on a number line?

**Tip:** When comparing square roots, it's helpful to memorize common approximations such as \( \sqrt{2} \approx 1.414 \) and \( \sqrt{3} \approx 1.732 \).

Place the numbers below in order from least to greatest. Which number will go in the yellow box? The numbers are: -√2, √3, 1.5, -1.6, -√3.

Learn how to order real numbers, including square roots, from least to greatest. This example explores irrational numbers such as -√2, √3, and compares them with other real numbers like 1.5 and -1.6. Suitable for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation