Question

Find the product of square root 12 and 5/6 what type of number is it 2.8867.... An irrational number 2.63-07... Any irrational number 4.1569 and irrational number 4.2974 and irrational number

Answer 1

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

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

Now, we can multiply \(2\sqrt{3}\) by \(\frac{5}{6}\):

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

Next, we need to approximate the value of \(\sqrt{3}\):

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

Thus:

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

The approximate value we get is \(2.8867\). This value is a non-repeating, non-terminating decimal, indicating that it is an **irrational number**.

Among the options you provided:

- \(2.8867...\) is an irrational number.
- \(2.63-07...\) is not clearly defined and might mean \(2.6307...\), which could also be a decimal approximation.
- \(4.1569\) appears to be rational.
- \(4.2974\) also appears to be rational.

Thus, the value \(2.8867...\) is indeed closest to the product we calculated and is classified as an **irrational number**.