Question

find the product of √12 and 5/6. what kind of number is it?
A. 4.1569 . . . ; an irrational number
B. 2.8867 . . . ; 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 \( \frac{5}{6} \):

1. Calculate \( \sqrt{12} \):
\[
\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}
\]

2. Now multiply \( 2\sqrt{3} \) by \( \frac{5}{6} \):
\[
2\sqrt{3} \times \frac{5}{6} = \frac{10\sqrt{3}}{6} = \frac{5\sqrt{3}}{3}
\]

3. Now, approximate \( \sqrt{3} \):
\[
\sqrt{3} \approx 1.732
\]

4. Substitute \( \sqrt{3} \) into the product:
\[
\frac{5\sqrt{3}}{3} \approx \frac{5 \times 1.732}{3} \approx \frac{8.66}{3} \approx 2.8867
\]

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

Thus, the answer is:

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