Which pair of numbers are both between 6 and 7? O v36 and V49 O V30 and V42 O V42 and V48 V37 and V50

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter12: Quadratic Functions
Section12.6: Solving Problems Involving Quadratic Equations
Problem 13P
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### Question:
Which pair of numbers are both between 6 and 7?

### Options:
1. ○ √36 and √49
2. ○ √30 and √42
3. ○ √42 and √48
4. ○ √37 and √50

### Explanation:
To determine which pair of numbers both fall between 6 and 7, we need to evaluate the square roots of the numbers provided in each option.

1. **√36 and √49**:
   - √36 = 6
   - √49 = 7
   - Thus, this pair includes one number that is exactly 6 and another that is exactly 7, so both are not between 6 and 7.

2. **√30 and √42**:
   - √30 ≈ 5.48 (not between 6 and 7)
   - √42 ≈ 6.48 (between 6 and 7)
   - Thus, this pair has only one number between 6 and 7.

3. **√42 and √48**:
   - √42 ≈ 6.48 (between 6 and 7)
   - √48 ≈ 6.93 (between 6 and 7)
   - Thus, both numbers in this pair are between 6 and 7.

4. **√37 and √50**:
   - √37 ≈ 6.08 (between 6 and 7)
   - √50 ≈ 7.07 (not between 6 and 7)
   - Thus, this pair has only one number between 6 and 7.

### Correct Answer:
The correct pair of numbers that are both between 6 and 7 is found in option 3:
- √42 and √48.
Transcribed Image Text:### Question: Which pair of numbers are both between 6 and 7? ### Options: 1. ○ √36 and √49 2. ○ √30 and √42 3. ○ √42 and √48 4. ○ √37 and √50 ### Explanation: To determine which pair of numbers both fall between 6 and 7, we need to evaluate the square roots of the numbers provided in each option. 1. **√36 and √49**: - √36 = 6 - √49 = 7 - Thus, this pair includes one number that is exactly 6 and another that is exactly 7, so both are not between 6 and 7. 2. **√30 and √42**: - √30 ≈ 5.48 (not between 6 and 7) - √42 ≈ 6.48 (between 6 and 7) - Thus, this pair has only one number between 6 and 7. 3. **√42 and √48**: - √42 ≈ 6.48 (between 6 and 7) - √48 ≈ 6.93 (between 6 and 7) - Thus, both numbers in this pair are between 6 and 7. 4. **√37 and √50**: - √37 ≈ 6.08 (between 6 and 7) - √50 ≈ 7.07 (not between 6 and 7) - Thus, this pair has only one number between 6 and 7. ### Correct Answer: The correct pair of numbers that are both between 6 and 7 is found in option 3: - √42 and √48.
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