Question

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

A) 2.8867 . . . ; an irrational number

B) 4.1569 . . . ; an irrational number

C) 4.2974 . . . ; an irrational number

D) 2.6307 . . . ; an irrational number

Answer 1

To find the product of \(\sqrt{12}\) and \(\frac{5}{6}\), we will first calculate \(\sqrt{12}\):

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

Now, we will multiply this 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 evaluate \(\frac{5\sqrt{3}}{3}\) numerically. To do this, we can approximate \(\sqrt{3}\):

\[
\sqrt{3} \approx 1.732
\]

Thus,

\[
\frac{5\sqrt{3}}{3} \approx \frac{5 \times 1.732}{3} \approx \frac{8.66}{3} \approx 2.8867
\]

The result is approximately \(2.8867\), and since \(\sqrt{3}\) is an irrational number, the product \(\frac{5\sqrt{3}}{3}\) is also an irrational number.

So, the final answer is:

**A) 2.8867 . . . ; an irrational number**