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.