Question 1

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

The value of sqrt(10) is approximately 3.16, which places it clearly between the two reference points labeled P and Q.

A) To the left of point P

This option is incorrect because point P represents a value greater than 3.16. Since sqrt(10) is approximately 3.16, it cannot lie to the left of P.

B) Between points P and Q

This option is correct as sqrt(10) is approximately 3.16, which is indeed between the values assigned to points P and Q on the number line.

C) Between points Q and R

This option is incorrect since point Q corresponds to a value less than 3.16, making it impossible for sqrt(10) to lie between Q and R.

D) Between points R and S

This option is also incorrect as point R indicates a value that is greater than 3.16, meaning sqrt(10) cannot be positioned between R and S.

E) To the right of point S

This option is incorrect because point S, like point R, indicates a value that is greater than 3.16, thus excluding the possibility of sqrt(10) being to the right of S.

Conclusion

The correct answer is B, as sqrt(10) is approximately 3.16, which clearly places it between points P and Q on the number line. All other options fail because they either suggest locations that are too far left or right, beyond the actual value of sqrt(10).