Question

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

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

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

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

4.2974 . . . ; an irrational number

Answer 1

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

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

Next, we multiply this by \( 56 \):

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

Now, we need to approximate \( \sqrt{3} \). The value of \( \sqrt{3} \) is approximately \( 1.732 \). Therefore:

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

Since \( 112\sqrt{3} \) is the product, we can conclude that this number is irrational because it involves \( \sqrt{3} \), which is an irrational number.

The actual numerical answer is not one of the options explicitly given, but it should be noted that \( 112\sqrt{3} \) is indeed an irrational number.

None of the multiple-choice responses accurately match the product calculated. However, we can confirm that \( 112\sqrt{3} \) is irrational. If you meant to calculate or compare with the choices provided, please double-check the values or specify if there is a different operation you need assistance with.