Question

Find the product of the square root of 12 and 5/6 what type of number is it

Answer 1

To find the product of the square root of 12 and \( \frac{5}{6} \), we first need to calculate \( \sqrt{12} \).

We can simplify \( \sqrt{12} \) as follows:

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

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

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

We can simplify \( \frac{10\sqrt{3}}{6} \):

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

Now, let's analyze the type of number \( \frac{5\sqrt{3}}{3} \). The term \( \sqrt{3} \) is an irrational number, and multiplying or dividing an irrational number by a rational number (like \( \frac{5}{3} \)) still results in an irrational number. Therefore, \( \frac{5\sqrt{3}}{3} \) is also an irrational number.

In summary, the product of the square root of 12 and \( \frac{5}{6} \) is \( \frac{5\sqrt{3}}{3} \), and it is an **irrational number**.