Question

Sums & Products of Rational & Irrational Numbers Quick Check
5 of 55 of 5 Items
Question
Find the product of 12−−√
and 56
. What type of number is it?(1 point)
Responses

4.1569 . . . ; an irrational number
4.1569 . . . ; an irrational number

2.6307 . . . ; an irrational number
2.6307 . . . ; an irrational number

4.2974 . . . ; an irrational number
4.2974 . . . ; an irrational number

2.8867 . . . ; an irrational number



please choose an answer i give you

Answer 1

please use an option i gave you

Answer 2

To find the product of \( \sqrt{12} \) and \( 56 \), we can calculate it as follows:

\[
\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}
\]

Now, multiply it by \( 56 \):

\[
56 \cdot \sqrt{12} = 56 \cdot 2\sqrt{3} = 112 \sqrt{3}
\]

Since \( \sqrt{3} \) is an irrational number, \( 112\sqrt{3} \) is also an irrational number.

Now, let's evaluate the possible answers. None of the responses provided seem to match the exact product \( 112\sqrt{3} \) or its numerical approximation:

- Approximately, \( 112\sqrt{3} \approx 112 \cdot 1.732 \approx 193.776 \)

None of the options provided in your question give that answer, as they all appear to be small decimal approximations.

However, they all state "an irrational number." Given this, the answer should point out that the product is indeed an irrational number, but the exact numeric options given do not match.

If you still want to pick one of the responses, you could choose any of the irrational options since they all state that the result is irrational. Would you like to choose one of them?