The side length of a square is equal to ?–.

  A. the square of its area

  B. the square root of its area

  C. its area

  D. half of its area

Which of the following statements is true?

  A. The square root of an integer will always be an integer.

  B. The square of an integer will always be an integer.

  C. Both A and B are true.

  D. Neither A nor B are true.

Which of the following numbers has a square root of 9?

  A. 3

  B. 4.5

  C. 18

  D. 81

Which of the following numbers is a perfect square?

  A. 2

  B. 8

  C. 16

  D. 20

Which of the following statements is true about the square root of 139?

  A. The square root of 139 has a value of 19,321.

  B. The square root of 139 has a value of 69.5.

  C. The square root of 139 has a value between 10 and 11.

  D. The square root of 139 has a value between 11 and 12.

Let's go through each question and determine the correct answers.

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### 1. The side length of a square is equal to?
For a square, if the area is \( A \) and the side length is \( s \), then the area \( A \) is given by \( A = s^2 \). Solving for \( s \), we find \( s = \sqrt{A} \).

**Correct answer: B. the square root of its area**

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### 2. Which of the following statements is true?
- **A.** The square root of an integer will not always be an integer (e.g., \( \sqrt{2} \) is not an integer).
- **B.** The square of an integer will always be an integer (e.g., \( 2^2 = 4 \), which is an integer).

**Correct answer: B. The square of an integer will always be an integer**

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### 3. Which of the following numbers has a square root of 9?
The number whose square root is 9 must be \( 9^2 = 81 \).

**Correct answer: D. 81**

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### 4. Which of the following numbers is a perfect square?
A perfect square is an integer that can be expressed as the square of another integer:
- 16 is \( 4^2 \), so it is a perfect square.

**Correct answer: C. 16**

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### 5. Which of the following statements is true about the square root of 139?
To estimate, note that:
- \( 11^2 = 121 \) and \( 12^2 = 144 \).
- Thus, \( \sqrt{139} \) lies between 11 and 12.

**Correct answer: D. The square root of 139 has a value between 11 and 12**

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Would you like further explanations on any of these answers, or do you have any questions?

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### Related Questions
1. What is the formula to calculate the area of a square given its side length?
2. Can a negative integer have an integer square root?
3. Why is the square of any real number always non-negative?
4. How can you identify a perfect square quickly?
5. How can we approximate square roots for non-perfect squares like 139?

**Tip:** When estimating square roots, remember the squares of numbers around the target for a quick estimate of the range.

The side length of a square is equal to? A. the square of its area B. the square root of its area C. its area D. half of its area. Which of the following statements is true? A. The square root of an integer will always be an integer. B. The square of an integer will always be an integer. C. Both A and B are true. D. Neither A nor B are true. Which of the following numbers has a square root of 9? A. 3 B. 4.5 C. 18 D. 81. Which of the following numbers is a perfect square? A. 2 B. 8 C. 16 D. 20. Which of the following statements is true about the square root of 139? A. The square root of 139 has a value of 19,321. B. The square root of 139 has a value of 69.5. C. The square root of 139 has a value between 10 and 11. D. The square root of 139 has a value between 11 and 12.

Explore key math concepts involving square roots, perfect squares, and square side length relationships. This problem includes examples on determining the side length of a square from its area, properties of integer squares, and estimating square roots, such as finding values between 10 and 11 or between 11 and 12. Ideal for students in Grades 6-8.

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