√(45) is between what two consecutive whole numbers?

Rationale

√(45) is between 6 and 7.

The square root of 45 is approximately 6.708, which lies between the whole numbers 6 and 7. This range can be confirmed by calculating the squares of both numbers: 6² = 36 and 7² = 49, indicating that √(45) falls within this interval.

A (4 and 5) YOUR ANSWER

The square of 4 is 16 and the square of 5 is 25. Since 45 is much larger than both 16 and 25, this option does not accurately represent the range in which √(45) lies.

B (5 and 6) YOUR ANSWER

The square of 5 is 25 and the square of 6 is 36. As 45 exceeds 36, this choice cannot be correct as it does not encapsulate √(45) within its boundaries.

C (6 and 7) CORRECT

The square of 6 is 36 and the square of 7 is 49. Since √(45) is approximately 6.708, it indeed falls between these two whole numbers, making this the correct answer.

D (14 and 15) YOUR ANSWER

The squares of 14 and 15 are 196 and 225, respectively. As 45 is significantly less than both of these values, this option is clearly incorrect.

E (22 and 23) YOUR ANSWER

The square of 22 is 484 and the square of 23 is 529. Given that 45 is far less than both of these values, this choice does not reflect the proper range for √(45).

Conclusion

To determine where √(45) lies, we assess the squares of whole numbers surrounding it. The calculated value of approximately 6.708 confirms that it is indeed between the consecutive whole numbers 6 and 7. Other options either fall below or far exceed this range, solidifying 6 and 7 as the correct interval for √(45).