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------------------------------------------------ Which of the following are equal to the expression below? Check all that apply.

\[ \sqrt{64} \cdot \sqrt{25} \]

A. \[ 5 \sqrt{64} \]
B. 40
C. 1600
D. \[ \sqrt{1600} \]
E. 89
F. \[ \sqrt{40} \]

To solve this problem, we need to determine which options are equal to the expression [tex]$\sqrt{64} \cdot \sqrt{25}$[/tex].

1. Calculate the expression:
[tex]\[
\sqrt{64} \cdot \sqrt{25}
\][/tex]
- First, find [tex]$\sqrt{64}$[/tex]. Since [tex]$64$[/tex] is a perfect square, [tex]$\sqrt{64} = 8$[/tex].
- Next, find [tex]$\sqrt{25}$[/tex]. Since [tex]$25$[/tex] is also a perfect square, [tex]$\sqrt{25} = 5$[/tex].
- Multiply the results: [tex]$8 \times 5 = 40$[/tex].

So, [tex]$\sqrt{64} \cdot \sqrt{25} = 40$[/tex].

2. Evaluate each option to see if it equals 40:

A. [tex]$5 \sqrt{64}$[/tex]
- Calculate [tex]$\sqrt{64}$[/tex]: [tex]$8$[/tex], then [tex]$5 \times 8 = 40$[/tex],
- So option A is equal to 40.

B. 40
- This is exactly 40,
- So option B is equal to 40.

C. 1600
- This is not equal to 40, so option C does not match.

D. [tex]$\sqrt{1600}$[/tex]
- Calculate [tex]$\sqrt{1600}$[/tex]. Since [tex]$1600$[/tex] is a perfect square, [tex]$\sqrt{1600} = 40$[/tex],
- So option D is equal to 40.

E. 89
- This number does not equal 40, so option E does not match.

F. [tex]$\sqrt{40}$[/tex]
- Calculate [tex]$\sqrt{40}$[/tex]. Since [tex]$40$[/tex] is not a perfect square, [tex]$\sqrt{40}$[/tex] is not equal to 40,
- So option F does not match.

3. Conclusion:
The options that equal the expression [tex]$\sqrt{64} \cdot \sqrt{25}$[/tex] are A, B, and D.