Between which two numbers will the square root of 10 lie on the number line?
Responses:
a) 10 and 10.5
b) pi and 4
c) 0 and pi
d) 14/5 and 31/10
To find the range of the square root of 10 on the number line, we can approximate its value. The square root of 10 is approximately 3.16.
Out of the given options, the only range that includes 3.16 is option (d) 14/5 and 31/10. Therefore, the square root of 10 lies between 14/5 and 31/10 on the number line.
To find the square root of 10, we can use estimation. The exact value of the square root of 10 is approximately 3.16227766017.
Among the options given, let's check which range includes this approximate value:
a) 10 and 10.5: The square root of 10 is less than 10.5, so this range includes the square root of 10.
b) pi and 4: The approximate value of the square root of 10 is less than pi but greater than 4, so this range does not include the square root of 10.
c) 0 and pi: The approximate value of the square root of 10 is less than pi, so this range includes the square root of 10.
d) 14/5 and 31/10: The approximate value of the square root of 10 is greater than the range given, so this range does not include the square root of 10.
Based on the above analysis, the square root of 10 lies between 10 and 10.5 on the number line. Therefore, the correct option is a) 10 and 10.5.