Pick One

Question

Find the product of 12−−√ and 56. What type of number is it?(1 point)
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 first calculate $\sqrt{12}$:

$$\sqrt{12}=\sqrt{4\times 3}=\sqrt{4}\times \sqrt{3}=2\sqrt{3}$$

Now, we multiply $2\sqrt{3}$ by $56$:

$$2\sqrt{3}\times 56=112\sqrt{3}$$

Next, we can approximate $\sqrt{3}$ to calculate $112\sqrt{3}$:

$$\sqrt{3}\approx 1.732$$

Therefore,

$$112\sqrt{3}\approx 112\times 1.732\approx 193.184$$

So, the approximate value of the product is $193.184$, which is not listed in your options and does not match any of the provided decimal numbers. However, the product $112\sqrt{3}$ is indeed an irrational number since it involves the square root of 3.

If we strictly need to select from the provided options, it seems there is a misunderstanding or misrepresentation of the question, as none of those options accurately reflect the product of $56\sqrt{12}$.