Question

for each irrational number listed in the table below, identify the closest whole number to which it lies on a number line. select the correct circle in each row.
irrational numbers: (sqrt{200}), (pi + 2)
closest to which whole number?
10, 12, 14, 16, 18, 20

Explanation:

Step1: Analyze \(\sqrt{200}\)

First, simplify \(\sqrt{200}\). We know that \(\sqrt{200}=\sqrt{100\times2} = \sqrt{100}\times\sqrt{2}=10\sqrt{2}\approx10\times1.414 = 14.14\). Now, find the closest whole number to \(14.14\). The whole numbers around it are \(14\) and \(15\). The distance from \(14.14\) to \(14\) is \(14.14 - 14=0.14\), and to \(15\) is \(15 - 14.14 = 0.86\). So the closest whole number is \(14\).

Step2: Analyze \(\pi+2\)

We know that \(\pi\approx3.14\), so \(\pi + 2\approx3.14+2 = 5.14\). Wait, no, wait, maybe I misread the second irrational number. Wait, the table has \(\sqrt{200}\) and another one, maybe \(\pi + 2\)? Wait, \(\pi\approx3.14\), so \(\pi + 2\approx5.14\)? No, that can't be. Wait, maybe it's \(\pi\times2\)? Wait, no, the user's image shows "π + 2" or maybe "π × 2"? Wait, no, let's re - check. Wait, the first irrational number is \(\sqrt{200}\approx14.14\), closest to \(14\). The second one: if it's \(\pi + 2\), \(\pi\approx3.14\), so \(3.14 + 2=5.14\), closest to \(5\)? But the table has whole numbers \(10,12,14,16,18,20\)? Wait, maybe I misread the second irrational number. Wait, maybe it's \(\pi\times4\)? No, wait, the table's whole numbers are \(10,12,14,16,18,20\). Wait, maybe the second irrational number is \(\sqrt{196}=14\)? No, no. Wait, maybe the second one is \(\pi\times 4.5\)? No, this is confusing. Wait, no, let's focus on \(\sqrt{200}\) first. \(\sqrt{200}\approx14.14\), so the closest whole number is \(14\). So for \(\sqrt{200}\), we circle the circle under \(14\). For the other one, if it's, say, \(\pi + 12\)? No, this is unclear. Wait, maybe the second irrational number is \(\sqrt{169}=13\) no. Wait, maybe the user made a typo, but let's proceed with \(\sqrt{200}\). The closest whole number to \(\sqrt{200}\approx14.14\) is \(14\), so we select the circle under \(14\) for \(\sqrt{200}\).

Answer:

For \(\sqrt{200}\), the closest whole number is \(14\), so select the circle under \(14\) in its row. (For the other irrational number, if it's \(\pi + 2\), there's a mistake in the table's whole numbers as \(5\) is not there, but assuming the table is correct, maybe I misread the second irrational number. But for \(\sqrt{200}\), the answer is \(14\).)