Find the product of sqrt(12) and What type of number is it? (1 point) 5/6 4.1569an irrational number 8867an irrational number 2.6307an irrational number 4 2974an irrational number

Answer 1

To find the product of \(\sqrt{12}\) and the numbers given, we first calculate \(\sqrt{12}\):

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

Next, we will calculate the product of \(2\sqrt{3}\) with each of the numbers listed.

1. With \( \frac{5}{6} \): \[ 2\sqrt{3} \cdot \frac{5}{6} = \frac{10\sqrt{3}}{6} = \frac{5\sqrt{3}}{3} \]

   \(\frac{5\sqrt{3}}{3}\) is irrational because it is a non-integer multiple of \(\sqrt{3}\), which is itself irrational.

2. With \( 4.1569 \): \[ 2\sqrt{3} \cdot 4.1569 = 8.3138\sqrt{3} \]

   \(8.3138\sqrt{3}\) is also irrational for the same reason; it is a non-integer multiple of an irrational number.

3. With \( 8867 \): \[ 2\sqrt{3} \cdot 8867 = 17734\sqrt{3} \]

   As before, \(17734\sqrt{3}\) is irrational.

4. With \( 2.6307 \): \[ 2\sqrt{3} \cdot 2.6307 = 5.2614\sqrt{3} \]

   \(5.2614\sqrt{3}\) is irrational.

5. With \( 4 \): \[ 2\sqrt{3} \cdot 4 = 8\sqrt{3} \]

   Again, \(8\sqrt{3}\) is irrational.

6. With \( 2974 \): \[ 2\sqrt{3} \cdot 2974 = 5948\sqrt{3} \]

   \(5948\sqrt{3}\) is irrational as well.

Conclusion: The product of \(\sqrt{12}\) with any of the listed numbers results in an irrational number.