Question
I'm the product of square root 12 and 5/6 what type of number is it
Answers
GPT-4o mini
To find the product of \(\sqrt{12}\) and \(\frac{5}{6}\), we start by simplifying \(\sqrt{12}\):
\[
\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}
\]
Now, we can multiply \(2\sqrt{3}\) by \(\frac{5}{6}\):
\[
2\sqrt{3} \times \frac{5}{6} = \frac{2 \times 5}{6} \times \sqrt{3} = \frac{10}{6} \sqrt{3} = \frac{5}{3} \sqrt{3}
\]
Now let's analyze the number \(\frac{5}{3} \sqrt{3}\):
1. \(\sqrt{3}\) is an **irrational number**, meaning it cannot be expressed as a fraction.
2. When you multiply a rational number (\(\frac{5}{3}\)) by an irrational number (\(\sqrt{3}\)), the result is also an **irrational number**.
Thus, the product of \(\sqrt{12}\) and \(\frac{5}{6}\), which is \(\frac{5}{3} \sqrt{3}\), is an **irrational number**.
\[
\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}
\]
Now, we can multiply \(2\sqrt{3}\) by \(\frac{5}{6}\):
\[
2\sqrt{3} \times \frac{5}{6} = \frac{2 \times 5}{6} \times \sqrt{3} = \frac{10}{6} \sqrt{3} = \frac{5}{3} \sqrt{3}
\]
Now let's analyze the number \(\frac{5}{3} \sqrt{3}\):
1. \(\sqrt{3}\) is an **irrational number**, meaning it cannot be expressed as a fraction.
2. When you multiply a rational number (\(\frac{5}{3}\)) by an irrational number (\(\sqrt{3}\)), the result is also an **irrational number**.
Thus, the product of \(\sqrt{12}\) and \(\frac{5}{6}\), which is \(\frac{5}{3} \sqrt{3}\), is an **irrational number**.