24. √(45) is between what two consecutive whole numbers?
Answer: C
√(45) is between 6 and 7
The square root of 45 falls between the whole numbers 6 and 7, as 6² (36) is less than 45 and 7² (49) is greater than 45.
A) 4 and 5
Option A is incorrect because 4² equals 16 and 5² equals 25, which are both significantly less than 45. Therefore, √(45) cannot be between these two numbers.
B) 5 and 6
Option B is also incorrect. While 5² equals 25, which is less than 45, 6² equals 36, still not reaching 45. Thus, √(45) is not between 5 and 6.
C) 6 and 7
This option is correct. Since 6² equals 36 and 7² equals 49, √(45) is indeed between these two values, confirming that 6 is less than √(45) and √(45) is less than 7.
D) 14 and 15
Option D is incorrect as 14² equals 196 and 15² equals 225, both of which are far greater than 45. Therefore, √(45) cannot be situated between 14 and 15.
E) 22 and 23
Option E is also incorrect since 22² equals 484 and 23² equals 529, which are again much larger than 45, ruling out this range for √(45).
Conclusion
The correct answer is C) 6 and 7 because √(45) is accurately positioned between these two whole numbers, as demonstrated by the squares of 6 and 7. All other options either underestimate or overestimate the value of √(45), making them incorrect.