Between which pair of rational number on a number line does sqrt(38) lie?
A. Between 6.3 and 6.5
B. Between 19 and 19.2
C. Between 18.9 and 19.1
D. Between 6.1 and 6.2
To solve this problem, we need to find two rational numbers between which the square root of 38 lies.
Let's find the square root of 38. Using estimation, we know that 6^2 = 36 and 7^2 = 49. Therefore, the square root of 38 lies between 6 and 7.
Now, let's find two rational numbers between 6 and 7 by using decimal values:
A. Between 6.3 and 6.5: These numbers are closer to 6, so we can eliminate this option.
B. Between 19 and 19.2: These numbers are much larger than the square root of 38, so we can eliminate this option.
C. Between 18.9 and 19.1: These numbers are also much larger than the square root of 38, so we can eliminate this option.
D. Between 6.1 and 6.2: These numbers are closest to 6, so this is the correct option.
Therefore, the square root of 38 lies between 6.1 and 6.2.
Answer: D. Between 6.1 and 6.2