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

Answer 1

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

Answer 2

To find the product of \( \sqrt{12} \) and \( 56 \), we can start by calculating \( \sqrt{12} \).

1. First, simplify \( \sqrt{12} \):
\[
\sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}
\]

2. Now find the product with \( 56 \):
\[
\sqrt{12} \times 56 = 2\sqrt{3} \times 56 = 112\sqrt{3}
\]

3. Now, let's calculate \( 112\sqrt{3} \) numerically. Knowing that \( \sqrt{3} \approx 1.732 \):
\[
112\sqrt{3} \approx 112 \times 1.732 \approx 193.824
\]

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

Now, since the question likely requires one of the given options, let's provide an approximate decimal value for \( 112\sqrt{3} \).
Calculating it more precisely:
\[
112 \times 1.73205080757 \approx 193.828
\]

None of the options you provided directly matches this value, but the important conclusion here is that the product of \( \sqrt{12} \) and \( 56 \) results in an irrational number.

Thus, the answer would be:
- The product \( 112\sqrt{3} \), an irrational number.

If you need to choose one of the provided options, please check again, as it looks like the products provided don't match the calculated value.