To determine between which two consecutive whole numbers the square root of 39 lies, we follow these steps:
1. Calculate the square root of 39.
The square root of 39 is approximately [tex]\( 6.245 \)[/tex].
2. Identify the two consecutive whole numbers between which this value falls.
- The whole number just below 6.245 is 6.
- The whole number just above 6.245 is 7.
3. Verify that 6 and 7 are indeed the correct bounds by calculating their squares:
- [tex]\( 6^2 = 36 \)[/tex]
- [tex]\( 7^2 = 49 \)[/tex]
4. Confirm that 39 lies between these squares:
- [tex]\( 36 < 39 < 49 \)[/tex]
Therefore, the two consecutive whole numbers between which [tex]\( \sqrt{39} \)[/tex] lies are 6 and 7. Hence, the correct choice is:
6 and 7 because 39 falls between [tex]\( 6^2=36 \)[/tex] and [tex]\( 7^2=49 \)[/tex].
