Find the product of 12−−√ and 5/6 . What type of number is it?(1 point)Responses

Answer 1

To find the product of \( \sqrt{12} \) and \( \frac{5}{6} \), we can calculate it as follows:

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

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

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

The result \( \frac{5}{3} \sqrt{3} \) is an irrational number because it is a product of a rational number \( \frac{5}{3} \) and an irrational number \( \sqrt{3} \).

Thus, the product of \( \sqrt{12} \) and \( \frac{5}{6} \) is \( \frac{5}{3} \sqrt{3} \), which is an irrational number.