Which factors of the base would help simplify the expression 1614

Question

?(1 point)
Responses

16=4⋅4
16 equals 4 times 4

16=4⋅2⋅2
16 equals 4 times 2 times 2

16=2⋅2⋅2⋅2
16 equals 2 times 2 times 2 times 2

16=8⋅8
16 equals 8 times 8

Answer 1

To simplify the expression $\sqrt{1614}$, we can factor the base $16$ into its prime factors. The correct factorization of $16$ is:

$$16=2^4=2\times 2\times 2\times 2$$

So from the options provided, the factors of the base that would help simplify the expression are:

$$16=2\cdot 2\cdot 2\cdot 2$$

This is the most helpful in finding the square root of $16$, as it shows how the number can be broken down into its prime factors.

While the other options are valid factorizations (like $4\cdot 4$ and $8\cdot 8$), they are not as straightforward for simplifying square roots as the $2\cdot 2\cdot 2\cdot 2$ factorization, which clearly shows its powers of 2.