Question 6

The principal square roots of 64 and 16 are 8 and 4.

The square root of 64 is 8, and the square root of 16 is 4, making these values the principal square roots of the respective numbers.

A) 8 and 4

This option is correct because the principal square root of 64 is indeed 8, and the principal square root of 16 is 4. Both values are non-negative and accurately represent the square roots of the provided numbers.

B) 32 and 8

This option is incorrect. While 8 is the correct square root of 16, 32 is not a square root of 64. The square root of 64 is 8, not 32; hence this pair does not satisfy the question.

C) 4 and 16

This option is also incorrect. The number 4 is the square root of 16, but 16 is not a square root of 64; rather, it is the original number. The correct square root of 64 is 8, making this option invalid.

D) 8 and 2

This option is incorrect as well. Although 8 is the correct square root of 64, 2 is not a square root of 16. The principal square root of 16 is 4, not 2, which makes this option false.

Conclusion

Option A is definitively correct as it accurately identifies the principal square roots of 64 and 16 as 8 and 4, respectively. All other options fail to provide the correct roots, either presenting incorrect values or misidentifying the square roots of the given numbers.