To determine which product is rational, we need to analyze each option:
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8 times square root of 25: \[ 8 \times \sqrt{25} = 8 \times 5 = 40 \] This is rational.
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12 times pi: \[ 12 \times \pi \] Since \(\pi\) is an irrational number, this product (12 times an irrational number) is irrational.
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10 times square root of 8: \[ 10 \times \sqrt{8} = 10 \times \sqrt{4 \times 2} = 10 \times 2\sqrt{2} = 20\sqrt{2} \] Since \(\sqrt{2}\) is an irrational number, this product is also irrational.
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12 ⋅ 5.3420941...: This product involves a decimal (5.3420941...), assuming it is a non-repeating, non-terminating decimal, it would be considered irrational. Therefore: \[ 12 \times 5.3420941... \] would also be irrational if 5.3420941... is not a terminating decimal.
Of all the options, the only rational product is 8 times square root of 25, which equals 40.