To find the product of \( \sqrt{12} \) and \( 56 \):
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First, calculate \( \sqrt{12} \): \[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \]
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Now, multiply \( 2\sqrt{3} \) by \( 56 \): \[ 2\sqrt{3} \times 56 = 112\sqrt{3} \]
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Next, to find an approximate decimal value of \( 112\sqrt{3} \), we can use the approximate value of \( \sqrt{3} \approx 1.732 \): \[ 112\sqrt{3} \approx 112 \times 1.732 \approx 193.184 \]
Since the product \( 112\sqrt{3} \) is expressed with an irrational number \( \sqrt{3} \), the product itself is also an irrational number.
None of the responses provided seem to match this calculation directly because the values calculated and their respective classifications as irrational were not listed in the options. However, it is important to note that the product \( 112\sqrt{3} \) is indeed an irrational number.
If you are looking for a response from listed options, please clarify.