On the number line above, where does the number sqrt(10) lie?

Rationale

sqrt(10) lies between points P and Q on the number line.

The square root of 10 is approximately 3.16, which places it between the values represented by points P (which is 3) and Q (which is 4) on the number line. This positioning reflects its numerical value, as it is greater than 3 but less than 4.

A (To the left of point P) YOUR ANSWER

This option suggests that sqrt(10) is less than 3, which is incorrect. Since sqrt(10) is approximately 3.16, it is clearly greater than point P, which is at 3.

B (Between points P and Q) CORRECT

This is the correct answer because sqrt(10) is approximately 3.16, placing it between point P (3) and point Q (4). This range accurately represents the location of sqrt(10) on the number line.

C (Between points Q and R) YOUR ANSWER

This choice indicates that sqrt(10) is greater than 4, which is not true, as sqrt(10) is approximately 3.16. Therefore, it cannot be between points Q (4) and R.

D (Between points R and S) YOUR ANSWER

This option implies that sqrt(10) is greater than the value represented by point R. Since point R is greater than 4, and sqrt(10) is approximately 3.16, this statement is incorrect.

E (To the right of point S) YOUR ANSWER

This choice suggests that sqrt(10) is greater than point S, which is also incorrect. Since point S represents a value greater than 4, and sqrt(10) is approximately 3.16, it is not to the right of point S.

Conclusion

The position of sqrt(10) on the number line is accurately described by the option indicating it lies between points P and Q. This reflects its approximate value of 3.16, verifying that it is greater than 3 but less than 4. All other options misrepresent the numerical value of sqrt(10) relative to the defined points on the number line.

On the number line above, where does the number sqrt(10) lie?

sqrt(10) lies between points P and Q on the number line.

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