Find the product of 12−−√

Question

and 56
. What type of number is it?(1 point)
Responses

4.2974 . . . ; an irrational number
4.2974 . . . ; an irrational number

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

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

2.8867 . . . ; an irrational number

Answer 1

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

1. Calculate \( \sqrt{12} \): \[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3} \]

2. Now, multiply \( 2\sqrt{3} \) by \( 56 \): \[ 56 \cdot 2\sqrt{3} = 112\sqrt{3} \]

3. To approximate the value of \( 112\sqrt{3} \), we use the approximate value of \( \sqrt{3} \approx 1.732 \): \[ 112\sqrt{3} \approx 112 \cdot 1.732 = 193.184 \]

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

Thus, the product \( 112\sqrt{3} \) is an irrational number, but we do not have a specific decimal approximation that matches the options provided. The calculations might point towards a mistake in finding the numerical representation, so let's verify our number choices again with standard decimal approximations.

The irrational product can be represented numerically but not directly equal to a finite decimal, confirming its nature as irrational. If you provide me with a point of reference or more context about how these values align, I can give clearer guidance. But for now, the final result is that \( 112\sqrt{3} \) is an irrational number.

Answer 2

just choose an answer that makes better sense please

Answer 3

Given the product is \( 112\sqrt{3} \), we can approximate \( 112\sqrt{3} \):

1. Approximating \( \sqrt{3} \): \[ \sqrt{3} \approx 1.732 \]
2. Multiplying: \[ 112 \times 1.732 \approx 193.184 \]

None of the provided numerical options match our calculation directly, but since all the answers indicate they are irrational numbers, we can infer that the product remains irrational due to the presence of the square root.

If forced to choose one from the options based on an approximation:

• Since \( 2.8867...\) is the smallest among options and could be in proximity to computations, we can opt for it, yet it's essential to acknowledge it's significantly smaller than expected.

Thus, the nearest option might be:

2.8867 . . . ; an irrational number