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

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

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

2.6307 . . . ; an irrational number

Answer 1

just pick one of these answers
4.1569 . . . ; an irrational number
4.1569 . . . ; an irrational number

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

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

2.6307 . . . ; an irrational number

Answer 2

To find the product of \( \sqrt{12} \) and \( 56 \), we can first simplify \( \sqrt{12} \):

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

Now, multiply this by \( 56 \):

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

Now, we need to approximate \( \sqrt{3} \) to determine the product's numerical value. The approximate value of \( \sqrt{3} \) is around \( 1.732 \).

Thus:

\[
112\sqrt{3} \approx 112 \times 1.732 \approx 193.184
\]

Now, since \( 112\sqrt{3} \) contains \( \sqrt{3} \), which is irrational, the whole product \( 112\sqrt{3} \) is also irrational.

Given the options you provided, none of them seem to resemble \( 112\sqrt{3} \) directly. However, we know that the product \( 112\sqrt{3} \) is irrational.

So while we can't match it directly to the approximations given, we can conclude that the product is an irrational number.

If you need to select one from the provided options:

- The type of number is **irrational**, regardless of the specific decimal approximation. The correct answer depends on potentially the closest approximation, but the key takeaway is that the product is an **irrational number**.