https://file.aiquickdraw.com/mathbot/file/17342583927523ihtu6tt.jpg

Let's analyze and solve the questions step by step.

---

### **Question 4**  
"Draw a ring around the expressions that are equal to \( 6^2 \)."

We know:
\[
6^2 = 6 \times 6 = 36
\]

- \( 6 \times 2 = 12 \) → **Not equal to 36**  
- \( 6 \times 6 = 36 \) → **Equal to \( 6^2 \)**  
- \( 6 + 6 = 12 \) → **Not equal to 36**  
- \( 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2^6 = 64 \) → **Not equal to 36**  
- \( 6 + 6 + 6 + 6 + 6 + 6 = 36 \) → **Equal to \( 6^2 \)**  

**Answers to be circled**:  
- \( 6 \times 6 \)  
- \( 6 + 6 + 6 + 6 + 6 + 6 \)  

---

### **Question 5**  
Annie and Heidi play "What’s my number?"  
- The number is **not less than 50**.  
- The number is **not more than 100**.  
- The number is **a cube number**.

From this, the number must be:  
- Between \( 50 \) and \( 100 \).  
- A **perfect cube**.

The perfect cubes in this range are:  
\[
3^3 = 27 \quad (less~than~50), \quad 4^3 = 64, \quad 5^3 = 125 \quad (more~than~100)
\]

Thus, the number is:
\[
\boxed{64}
\]

---

### **Practice Question (6)**  
"A number is squared, and then 2 is added. The answer is 6."

Let the unknown number be \( x \).  
The equation becomes:
\[
x^2 + 2 = 6
\]

1. Subtract 2 from both sides:
\[
x^2 = 6 - 2 \implies x^2 = 4
\]

2. Solve for \( x \) by taking the square root:
\[
x = \pm \sqrt{4} \implies x = \pm 2
\]

Thus, the possible number is:
\[
\boxed{2}
\]
(Since it’s likely considering only positive values in this context.)

---

### **Summary of Answers**  
1. **Question 4**: \( 6 \times 6 \) and \( 6 + 6 + 6 + 6 + 6 + 6 \)  
2. **Question 5**: \( 64 \)  
3. **Question 6**: \( 2 \)  

---

### **Follow-Up Questions**
1. How do you calculate cube roots of numbers?  
2. What are the first 10 perfect squares and perfect cubes?  
3. How do we check if a number lies between two given numbers?  
4. What happens if the condition \( x^2 + c = n \) changes?  
5. Can a number have more than one square root? Explain why.

### **Tip**  
To solve equations like \( x^2 + c = n \), always isolate \( x^2 \) first and then take the square root, remembering to include both positive and negative roots.

Let me know if you need more details! 😊

Draw a ring around the expressions that are equal to 6². Annie and Heidi play 'What's my number?' game where the conditions are: The number is not less than 50, not more than 100, and it is a cube number. A number is squared and 2 is added, resulting in 6. Find the number.

Learn how to determine which expressions equal 6², find cube numbers between 50 and 100, and solve basic algebraic equations involving squares. This guide includes detailed solutions for students in Grades 5-7.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation