Question

Find the product of 12−−√ and 56. What type of number is it?(1 point)

Responses

#1 4.2974 . . . ; an irrational number

#2 4.1569 . . . ; an irrational number

#3 2.8867 . . . ; an irrational number

#4 2.6307 . . . ; an irrational number

Answer 1

To find the product of \( \sqrt{12} \) and \( 56 \), we can start by calculating \( \sqrt{12} \).

We know that:
\[
\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}.
\]

Now, we can calculate the product:
\[
\sqrt{12} \times 56 = 2\sqrt{3} \times 56 = 112\sqrt{3}.
\]

Next, we can estimate the value of \( \sqrt{3} \):
\[
\sqrt{3} \approx 1.732.
\]

Therefore, we can find \( 112\sqrt{3} \) by multiplying:
\[
112 \times 1.732 \approx 193.184.
\]

Since \( 112\sqrt{3} \) is a product of a rational number (112) and an irrational number (\( \sqrt{3} \)), the result \( 112\sqrt{3} \) is also irrational.

Looking at your provided responses, none of them list \( 193.184 \) as an option. However, since \( 112\sqrt{3} \) is irrational, it confirms that the product is an irrational number. Without an exact match in the product value, the most pertinent information is that the product is:

**Answer:** \( 112\sqrt{3} \); an irrational number.