Question

Find the product of 12−−√ and 5/6 . What type of number is it?(1 point)
Responses

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

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

Answer 1

To find the product of \( \sqrt{12} \) and \( \frac{5}{6} \), we first compute \( \sqrt{12} \).

We know that:
\[
\sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}
\]

Next, we multiply \( 2\sqrt{3} \) by \( \frac{5}{6} \):
\[
2\sqrt{3} \times \frac{5}{6} = \frac{10\sqrt{3}}{6} = \frac{5\sqrt{3}}{3}
\]

Now, we need to compute the approximate value of \( \frac{5\sqrt{3}}{3} \). Given that \( \sqrt{3} \approx 1.732 \):
\[
\frac{5 \times 1.732}{3} = \frac{8.66}{3} \approx 2.8867
\]

Thus, the product \( \frac{5\sqrt{3}}{3} \approx 2.8867 \).

Since \( \sqrt{3} \) is an irrational number, any product of an irrational number and a non-zero rational number is also irrational.

The final result is:
\[
2.8867... ; \text{ an irrational number}
\]

Therefore, the correct response is:
**2.8867 . . . ; an irrational number**