Question

sums & products of rational & irrational numbers
find the product of \\(\sqrt{12}\\) and \\(\frac{5}{6}\\). what type of number is it? (1 point)
\\(\circ\\) 4.1569 . . . ; an irrational number
\\(\circ\\) 4.2974 . . . ; an irrational number
\\(\circ\\) 2.8867 . . . ; an irrational number
\\(\circ\\) 2.6307 . . . ; an irrational number

Explanation:

Step1: Simplify $\sqrt{12}$

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

Step2: Calculate the product

$\sqrt{12} \times \frac{5}{6} = 2\sqrt{3} \times \frac{5}{6} = \frac{10\sqrt{3}}{6} = \frac{5\sqrt{3}}{3}$

Step3: Compute decimal approximation

Since $\sqrt{3} \approx 1.732$, $\frac{5 \times 1.732}{3} = \frac{8.66}{3} \approx 2.8867$

Step4: Classify the number

$\sqrt{3}$ is irrational, so $\frac{5\sqrt{3}}{3}$ is irrational.

Answer:

2.8867 . . . ; an irrational number