Question
Find the product of 12−−√ and 5/6 . What type of number is it?(1 point)Responses
Answers
GPT-4o mini
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.
\[
\sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}
\]
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.