Representing Real Numbers on the Number Line MCQs

Q1. On the number line, sqrt(7) falls between which two consecutive integers?

• A.2 and 3
• B.1 and 2
• C.3 and 4
• D.6 and 7

Answer: A. 2 and 3

Q2. On the number line, sqrt(13) falls between which two consecutive integers?

• A.3 and 4
• B.2 and 3
• C.4 and 5
• D.12 and 13

Answer: A. 3 and 4

Given 13, asked for the unknown. Apply the standard chapter relation to the data. 3^2 = 9 → 4^2 = 16. so sqrt(13) is between 3 and 4. Putting it together option A) 3 and 4. Others fail: option B) '2 and 3' is incorrect: 3^2 = 9 < 13, 4^2 = 16 > 13; option C) '4 and 5' misses the point - 3^2 = 9 < 13 but 4^2 = 16 >= 13.

Q3. On the number line, sqrt(19) falls between which two consecutive integers?

• A.4 and 5
• B.3 and 4
• C.5 and 6
• D.18 and 19

Answer: A. 4 and 5

Quick parse - a typical math numerical. The data on the table: 19. We are after the quantity the stem asks for. Pick the chapter relation that contains every given quantity and the unknown; rearrange for the unknown. Numbers in: 4^2 = 16 → 5^2 = 25. Common-sense check: so sqrt(19) is between 4 and 5. Lock in option A) 4 and 5. Trap-watch: option B) '3 and 4' doesn't hold - 4^2 = 16 < 19, 5^2 = 25 > 19; option C) '5 and 6' is incorrect: 4^2 = 16 < 19 but 5^2 = 25 >= 19.