What are the principal square roots of 64 and 16?

Rationale

8 and 4 are the principal square roots of 64 and 16, respectively.

The principal square root of a number is the non-negative value that, when multiplied by itself, gives the original number. For 64, the square root is 8, and for 16, it is 4, making the pair (8, 4) the correct answer.

A (8 and 4) CORRECT

The square root of 64 is 8 because \(8 \times 8 = 64\), and the square root of 16 is 4 since \(4 \times 4 = 16\). This choice accurately reflects the principal square roots for both numbers.

B (32 and 8) YOUR ANSWER

The number 32 is incorrect as the square root of 64. In fact, \(32 \times 32 = 1024\), which is far greater than 64. Hence, this option does not provide the correct principal square roots for either 64 or 16.

C (4 and 16) YOUR ANSWER

This choice incorrectly identifies the square root of 64 as 4 and the square root of 16 as 16. While 4 is indeed the square root of 16, it does not apply to 64, where the correct square root is 8. Thus, this option is incorrect.

D (8 and 2) YOUR ANSWER

While 8 is the correct square root of 64, 2 is incorrectly presented as the square root of 16. The correct square root of 16 is 4, not 2, making this option incorrect.

Conclusion

The principal square roots of 64 and 16 are 8 and 4, respectively, as these values satisfy the definition of square roots for their respective numbers. The other options incorrectly represent the square roots, either by miscalculating or providing non-matching pairs. Understanding square roots is fundamental in mathematics, particularly in solving equations and simplifying expressions.

What are the principal square roots of 64 and 16?

8 and 4 are the principal square roots of 64 and 16, respectively.

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