Question

Find the product of 12−−√
and 56
. What type of number is it?(1 point)
Responses

2.8867 . . . ; an irrational number
2.8867 . . . ; an irrational number

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

Answer 1

To find the product of \( \sqrt{12} \) and \( 56 \), we first calculate \( \sqrt{12} \).

We know that:

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

Next, we compute the product:

\[
\sqrt{12} \times 56 = (2\sqrt{3}) \times 56 = 112\sqrt{3}
\]

Now we need to find the approximate value of \( 112\sqrt{3} \). The value of \( \sqrt{3} \) is approximately \( 1.732 \).

Now we calculate:

\[
112 \times 1.732 \approx 193.984
\]

So, \( 112\sqrt{3} \approx 193.984 \), which is a whole number multiplied by an irrational number \( \sqrt{3} \).

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

The product \( 112\sqrt{3} \) is not one of the provided numerical options, but it is classified as an irrational number. Therefore, you can summarize the answer as follows:

- Approximately \( 193.984 \); an irrational number.

None of the provided options are correct as they do not match the calculated product.