Question

A) Which expression is equivalent to √600? (1 point)
6√10
10√6
24√25
25√24

Answer 1

To simplify \( \sqrt{600} \), we start by breaking down 600 into its prime factors:

\[
600 = 6 \times 100 = 6 \times 10^2
\]
Next, we can break down 6 further:
\[
6 = 2 \times 3 \implies 600 = 2 \times 3 \times 10^2
\]

Now, rewriting \( 600 \) as a product of its prime factors gives us:
\[
600 = 2^3 \times 3^1 \times 5^2
\]

We can then simplify \( \sqrt{600} \):
\[
\sqrt{600} = \sqrt{(2^2 \times 5^2) \times (2 \times 3)} = \sqrt{(10^2) \times (6)} = 10\sqrt{6}
\]

Thus, the expression equivalent to \( \sqrt{600} \) is:

\[
10\sqrt{6}
\]

So the answer is:
**10√6**