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

1 answer

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.