To simplify the expression [tex]$\sqrt{32} \cdot 5 \sqrt{2}$[/tex], let's break it down step by step.
1. Simplify [tex]$\sqrt{32}$[/tex]:
- [tex]$\sqrt{32}$[/tex] can be expressed as [tex]$\sqrt{16 \cdot 2}$[/tex].
- We know that [tex]$\sqrt{16} = 4$[/tex], so [tex]$\sqrt{32} = \sqrt{16 \cdot 2} = 4 \sqrt{2}$[/tex].
2. Multiply by [tex]$5 \sqrt{2}$[/tex]:
- We already know that [tex]$\sqrt{32} = 4 \sqrt{2}$[/tex].
- Now, multiply this by [tex]$5 \sqrt{2}$[/tex].
- This can be written as [tex]$(4 \sqrt{2}) \cdot (5 \sqrt{2})$[/tex].
3. Combine the terms:
- Multiplying the numerical coefficients: [tex]$4 \cdot 5 = 20$[/tex].
- Multiplying the square roots: [tex]$\sqrt{2} \cdot \sqrt{2} = \sqrt{4} = 2$[/tex].
4. Final multiplication:
- So, [tex]$4 \sqrt{2} \cdot 5 \sqrt{2} = 20 \cdot 2 = 40$[/tex].
Therefore, the simplified form of the expression [tex]$\sqrt{32} \cdot 5 \sqrt{2}$[/tex] is [tex]$40$[/tex].
Thus, the correct answer is:
[tex]\[ \boxed{40} \][/tex]
