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

Question

Responses

2.8867 . . . ; an irrational number
2.8867 . . . ; an irrational number

4.1569 . . . ; an irrational number
4.1569 . . . ; an irrational number

2.6307 . . . ; an irrational number
2.6307 . . . ; an irrational number

4.2974 . . . ; an irrational number

Answer 1

To find the product of \( \sqrt{12} \) and \( 56 \), we can calculate it step by step.

First, let's simplify \( \sqrt{12} \): \[ \sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3} \]

Now, we calculate the product of \( \sqrt{12} \) and \( 56 \): \[ \sqrt{12} \cdot 56 = 2\sqrt{3} \cdot 56 = 112\sqrt{3} \]

Now, we need to find the approximate numerical value of \( 112\sqrt{3} \). The approximate value of \( \sqrt{3} \) is about \( 1.732 \): \[ 112 \cdot 1.732 \approx 193.184 \]

Since \( \sqrt{3} \) is an irrational number, the product \( 112\sqrt{3} \) is also irrational.

Looking at the given response options, none match the specific numerical value obtained, but we can conclude that the product is indeed an irrational number.

So, the type of number is an irrational number.