Question
Find the product of square root of 12 and 5/6. What type of number is it?but is it a rational number, irrational, whole number, or an integar
Answers
GPT-4o mini
To find the product of \(\sqrt{12}\) and \(\frac{5}{6}\), we start by simplifying \(\sqrt{12}\).
\[
\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}
\]
Next, we multiply \(2\sqrt{3}\) by \(\frac{5}{6}\):
\[
2\sqrt{3} \times \frac{5}{6} = \frac{2 \times 5}{6} \sqrt{3} = \frac{10}{6} \sqrt{3} = \frac{5}{3} \sqrt{3}
\]
Now we need to determine the type of number \(\frac{5}{3} \sqrt{3}\) is.
- \(\sqrt{3}\) is an **irrational number** because it cannot be expressed as a fraction of two integers.
- \(\frac{5}{3}\) is a **rational number** because it is in the form of a fraction of two integers.
The product of a rational number and an irrational number is **irrational**. Therefore, \(\frac{5}{3} \sqrt{3}\) is an **irrational number**.
In summary, the product of \(\sqrt{12}\) and \(\frac{5}{6}\) is \(\frac{5}{3} \sqrt{3}\), which is an **irrational number**.
\[
\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}
\]
Next, we multiply \(2\sqrt{3}\) by \(\frac{5}{6}\):
\[
2\sqrt{3} \times \frac{5}{6} = \frac{2 \times 5}{6} \sqrt{3} = \frac{10}{6} \sqrt{3} = \frac{5}{3} \sqrt{3}
\]
Now we need to determine the type of number \(\frac{5}{3} \sqrt{3}\) is.
- \(\sqrt{3}\) is an **irrational number** because it cannot be expressed as a fraction of two integers.
- \(\frac{5}{3}\) is a **rational number** because it is in the form of a fraction of two integers.
The product of a rational number and an irrational number is **irrational**. Therefore, \(\frac{5}{3} \sqrt{3}\) is an **irrational number**.
In summary, the product of \(\sqrt{12}\) and \(\frac{5}{6}\) is \(\frac{5}{3} \sqrt{3}\), which is an **irrational number**.
just give me what the decimal is without any complicated slashes
GPT-4o mini
The product of \(\sqrt{12}\) and \(\frac{5}{6}\) is approximately \(2.887\).