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Select the correct answer.

What is this expression in simplified form? [tex](8 \sqrt{10})(8 \sqrt{5})[/tex]

A. [tex]64 \sqrt{50}[/tex]

B. [tex]16 \sqrt{50}[/tex]

C. [tex]80 \sqrt{2}[/tex]

D. [tex]320 \sqrt{2}[/tex]


Sagot :

To simplify the expression \((8 \sqrt{10})(8 \sqrt{5})\), we can follow these steps:

1. Multiply the coefficients:
[tex]\[ 8 \times 8 = 64 \][/tex]

2. Multiply the square roots:
[tex]\[ \sqrt{10} \times \sqrt{5} = \sqrt{10 \times 5} = \sqrt{50} \][/tex]

3. Combine the results from steps 1 and 2:
[tex]\[ 64 \times \sqrt{50} \][/tex]

Therefore, an intermediate form of the expression is \(64 \sqrt{50}\).

Next, observe that \(\sqrt{50}\) can be further simplified:
[tex]\[ \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5 \sqrt{2} \][/tex]

Substitute this simplification back into the expression:
[tex]\[ 64 \sqrt{50} = 64 \times 5 \sqrt{2} = 320 \sqrt{2} \][/tex]

Thus, the simplified form of \((8 \sqrt{10})(8 \sqrt{5})\) is \(\boxed{320 \sqrt{2}}\).

So, the correct answer is:
[tex]\[ \boxed{D} \][/tex]