Question

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

A. 4.2974...; an irrational number

B. 2.8867...; an irrational number

C. 4.1569...; an irrational number

D. 2.6307...; an irrational number

Answer 1

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

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

Now, we multiply this by \( \frac{5}{6} \):

\[
\frac{5}{6} \times 2\sqrt{3} = \frac{10\sqrt{3}}{6} = \frac{5\sqrt{3}}{3}
\]

Next, we can approximate \( \sqrt{3} \) (which is an irrational number) with its decimal value. The approximate value of \( \sqrt{3} \) is about 1.732.

Calculating the product:

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

Now, looking at the options provided:

- A. 4.2974...; an irrational number
- B. 2.8867...; an irrational number
- C. 4.1569...; an irrational number
- D. 2.6307...; an irrational number

The closest match to our calculated value \( \approx 2.8867 \) is option **B. 2.8867...; an irrational number**. Thus, the answer is:

**B. 2.8867...; an irrational number**.