Let's break down the problem step-by-step to arrive at the most simplified form of the given expression [tex]\( (8 \sqrt{10})(8 \sqrt{5}) \)[/tex]:
1. Identify the components:
The expression consists of two products: [tex]\( 8 \sqrt{10} \)[/tex] and [tex]\( 8 \sqrt{5} \)[/tex].
2. Multiply the coefficients:
The coefficients are the numbers outside the square roots. Multiply these first:
[tex]\[
8 \times 8 = 64
\][/tex]
3. Multiply the radicands (numbers inside the square roots):
Multiply the radicands of the square roots:
[tex]\[
\sqrt{10} \times \sqrt{5} = \sqrt{10 \times 5} = \sqrt{50}
\][/tex]
4. Combine the results:
After multiplying the coefficients and the radicands, combine them to form the simplified expression:
[tex]\[
64 \sqrt{50}
\][/tex]
Thus, the simplified form of the expression [tex]\( (8 \sqrt{10})(8 \sqrt{5}) \)[/tex] is
[tex]\[
64 \sqrt{50}
\][/tex]
Therefore, the correct answer is:
A. [tex]\( 64 \sqrt{50} \)[/tex]
