https://file.aiquickdraw.com/mathbot/file/1727357729595s2jdzeag.jpg

Here are the answers and explanations for the questions shown in the image:

1. **Which of the following can be represented as a whole number?**
   - A. √7
   - B. √8
   - C. **√9** (Answer: C)
   - D. √10
   
   Explanation: √9 = 3, which is a whole number, whereas the square roots of 7, 8, and 10 are not whole numbers.

2. **What is the value of √49?**
   - A. 6
   - B. **7** (Answer: B)
   - C. 8
   - D. 9
   
   Explanation: √49 = 7.

3. **What is the value of √2,500?**
   - A. 5
   - B. **50** (Answer: C)
   - C. 25
   - D. 500
   
   Explanation: √2,500 = 50.

4. **Which of the following numbers is a perfect square?**
   - A. 625
   - B. 3,625
   - C. **4,000** (Answer: C)
   - D. 6,289
   
   Explanation: A perfect square is a number that can be expressed as the square of an integer. The number 4,000 is a perfect square (because √4000 = 20√10).

5. **Which of the following numbers is a perfect cube?**
   - A. 141
   - B. 500
   - C. 627
   - D. **729** (Answer: D)
   
   Explanation: A perfect cube is a number that can be expressed as the cube of an integer. 729 = 9^3, so it is a perfect cube.

6. **Which of the following is NOT equal to 2?**
   - A. 8/4
   - B. √4
   - C. ³√8
   - D. **³√4** (Answer: D)
   
   Explanation: 
   - 8/4 = 2
   - √4 = 2
   - ³√8 = 2 (the cube root of 8 is 2)
   - ³√4 ≠ 2 (the cube root of 4 is not equal to 2).

Would you like more details or have any further questions?

Here are five follow-up questions for practice:
1. What is the square root of 144?
2. What is the cube root of 27?
3. Which of the following is a perfect square: 81, 121, 169?
4. What is the value of ³√27?
5. If √16 = 4, what is √64?

**Tip:** Remember that square roots of perfect squares are always whole numbers.

Which of the following can be represented as a whole number, square roots and cube roots, as well as perfect cubes and perfect squares?

This math problem helps students determine which square and cube roots are whole numbers and which numbers are perfect squares or perfect cubes. Suitable for Grades 7-9, it includes examples like √49 = 7 and ³√729 = 9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation