Question 29

sqrt(45) is between 6 and 7

The value of sqrt(45) is approximately 6.71, which falls between the whole numbers 6 and 7.

A) 4 and 5

This option is incorrect because both 4 and 5 are too low. The square of 4 is 16, and the square of 5 is 25, neither of which approach 45. Therefore, sqrt(45) cannot fall between these two values.

B) 5 and 6

This option is also incorrect. The square of 5 is 25, and the square of 6 is 36, which are both below 45. Consequently, sqrt(45) cannot be between 5 and 6, as it exceeds these limits.

C) 6 and 7

This option is correct because the square of 6 is 36, and the square of 7 is 49. Since 45 lies between these two squares, sqrt(45) is indeed between 6 and 7.

D) 14 and 15

This option is incorrect because both 14 and 15 are significantly higher than the value of sqrt(45). The square of 14 is 196, and the square of 15 is 225, which are much greater than 45.

E) 22 and 23

This option is incorrect as well. The square of 22 is 484, and the square of 23 is 529, which are both far greater than 45. Therefore, sqrt(45) cannot be between these two numbers.

Conclusion

The correct answer is C) 6 and 7, as sqrt(45) is approximately 6.71, clearly placing it between these two consecutive whole numbers. All other options are incorrect because they either understate or overstate the square root of 45, failing to capture its true value.