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

Rationale

sqrt(45) is between 6 and 7.

The square root of 45 is approximately 6.708, which falls between the whole numbers 6 and 7. This can be confirmed by recognizing that 6^2 equals 36 and 7^2 equals 49, thus positioning sqrt(45) between these two values.

A (4 and 5) YOUR ANSWER

The square root of 45 is significantly larger than 5, as 5^2 equals 25. Therefore, it's impossible for sqrt(45) to be between 4 and 5, given that its value exceeds 6.

B (5 and 6) YOUR ANSWER

While 5 is less than sqrt(45), the square root is approximately 6.708, indicating that it is greater than 6. Consequently, sqrt(45) cannot be between 5 and 6.

C (6 and 7) CORRECT

This choice correctly identifies the range where sqrt(45) resides. With a calculated value of approximately 6.708, it is indeed between the whole numbers 6 and 7.

D (14 and 15) YOUR ANSWER

Both 14 and 15 are far above the value of sqrt(45). Since 14^2 equals 196 and 15^2 equals 225, it is clear that sqrt(45) is much lower than both numbers.

E (22 and 23) YOUR ANSWER

Similarly, 22 and 23 are also much higher than the value of sqrt(45). With 22^2 equal to 484 and 23^2 equal to 529, it is evident that sqrt(45) does not fall within this range.

Conclusion

The square root of 45 is approximately 6.708, placing it between the consecutive whole numbers 6 and 7. All other choices incorrectly suggest ranges that do not encompass the value of sqrt(45), further reinforcing that option C is the only accurate answer for this question.