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.